[{"data":1,"prerenderedAt":4546},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-tangens":546,"formula-related-de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-tangens":4533},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":554,"category":518,"checks":4469,"conditions":4500,"conditionsHtml":4501,"deprecated":4502,"description":4462,"extension":4503,"figure":4502,"figureCaption":4502,"figureHtml":4502,"formulaId":4504,"latex":4505,"latexHtml":4506,"level":4507,"meta":4508,"navigation":4509,"path":4510,"redirectFrom":4511,"related":4512,"seo":4517,"stem":4518,"subject":581,"summary":4519,"tags":4520,"variables":4525,"__hash__":4532},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-tangens.md","Doppelwinkelformel für den Tangens",[550,551,552,553],"tan(2x)","Doppelwinkelformel Tangens","Tangens des doppelten Winkels","tan 2x = 2 tan x \u002F (1 − tan² x)",{"type":555,"value":556,"toc":4461},"minimark",[557,562,754,757,1484,1488,1829,2238,2242,2319,2730,3051,3717,3721],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,570,571,651,652,694,695,753],"p",{},"Die ",[567,568,569],"strong",{},"Doppelwinkelformel"," drückt ",[572,573,576,617],"span",{"className":574},[575],"katex",[572,577,580],{"className":578},[579],"katex-mathml",[581,582,584],"math",{"xmlns":583},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[585,586,587,612],"semantics",{},[588,589,590,594,598,602,606,609],"mrow",{},[591,592,593],"mi",{},"tan",[595,596,597],"mo",{},"⁡",[595,599,601],{"stretchy":600},"false","(",[603,604,605],"mn",{},"2",[591,607,608],{},"x",[595,610,611],{"stretchy":600},")",[613,614,616],"annotation",{"encoding":615},"application\u002Fx-tex","\\tan(2x)",[572,618,622],{"className":619,"ariaHidden":621},[620],"katex-html","true",[572,623,626,631,635,639,643,647],{"className":624},[625],"base",[572,627],{"className":628,"style":630},[629],"strut","height:1em;vertical-align:-0.25em;",[572,632,593],{"className":633},[634],"mop",[572,636,601],{"className":637},[638],"mopen",[572,640,605],{"className":641},[642],"mord",[572,644,608],{"className":645},[642,646],"mathnormal",[572,648,611],{"className":649},[650],"mclose"," allein durch ",[572,653,655,673],{"className":654},[575],[572,656,658],{"className":657},[579],[581,659,660],{"xmlns":583},[585,661,662,670],{},[588,663,664,666,668],{},[591,665,593],{},[595,667,597],{},[591,669,608],{},[613,671,672],{"encoding":615},"\\tan x",[572,674,676],{"className":675,"ariaHidden":621},[620],[572,677,679,683,686,691],{"className":678},[625],[572,680],{"className":681,"style":682},[629],"height:0.6151em;",[572,684,593],{"className":685},[634],[572,687],{"className":688,"style":690},[689],"mspace","margin-right:0.1667em;",[572,692,608],{"className":693},[642,646]," aus. Sie ist der Sonderfall ",[572,696,698,718],{"className":697},[575],[572,699,701],{"className":700},[579],[581,702,703],{"xmlns":583},[585,704,705,715],{},[588,706,707,710,713],{},[591,708,709],{},"y",[595,711,712],{},"=",[591,714,608],{},[613,716,717],{"encoding":615},"y = x",[572,719,721,743],{"className":720,"ariaHidden":621},[620],[572,722,724,728,732,736,740],{"className":723},[625],[572,725],{"className":726,"style":727},[629],"height:0.625em;vertical-align:-0.1944em;",[572,729,709],{"className":730,"style":731},[642,646],"margin-right:0.0359em;",[572,733],{"className":734,"style":735},[689],"margin-right:0.2778em;",[572,737,712],{"className":738},[739],"mrel",[572,741],{"className":742,"style":735},[689],[572,744,746,750],{"className":745},[625],[572,747],{"className":748,"style":749},[629],"height:0.4306em;",[572,751,608],{"className":752},[642,646]," des Additionstheorems für den Tangens.",[563,755,756],{},"Sie gilt nur, wenn beide Seiten definiert sind:",[758,759,760,1034],"ul",{},[761,762,763,801,802,1033],"li",{},[572,764,766,783],{"className":765},[575],[572,767,769],{"className":768},[579],[581,770,771],{"xmlns":583},[585,772,773,781],{},[588,774,775,777,779],{},[591,776,593],{},[595,778,597],{},[591,780,608],{},[613,782,672],{"encoding":615},[572,784,786],{"className":785,"ariaHidden":621},[620],[572,787,789,792,795,798],{"className":788},[625],[572,790],{"className":791,"style":682},[629],[572,793,593],{"className":794},[634],[572,796],{"className":797,"style":690},[689],[572,799,608],{"className":800},[642,646]," muss existieren, also ",[572,803,805,848],{"className":804},[575],[572,806,808],{"className":807},[579],[581,809,810],{"xmlns":583},[585,811,812,845],{},[588,813,814,816,820,829,832,835,838],{},[591,815,608],{},[595,817,819],{"mathvariant":818},"normal","≠",[821,822,823,826],"msup",{},[603,824,825],{},"90",[595,827,828],{},"∘",[595,830,831],{},"+",[591,833,834],{},"k",[595,836,837],{},"⋅",[821,839,840,843],{},[603,841,842],{},"180",[595,844,828],{},[613,846,847],{"encoding":615},"x \\neq 90^\\circ + k \\cdot 180^\\circ",[572,849,851,910,974,994],{"className":850,"ariaHidden":621},[620],[572,852,854,858,861,864,907],{"className":853},[625],[572,855],{"className":856,"style":857},[629],"height:0.8889em;vertical-align:-0.1944em;",[572,859,608],{"className":860},[642,646],[572,862],{"className":863,"style":735},[689],[572,865,867,900,904],{"className":866},[739],[572,868,870],{"className":869},[739],[572,871,874],{"className":872},[642,873],"vbox",[572,875,878],{"className":876},[877],"thinbox",[572,879,882,885,896],{"className":880},[881],"rlap",[572,883],{"className":884,"style":857},[629],[572,886,889],{"className":887},[888],"inner",[572,890,892],{"className":891},[642],[572,893,895],{"className":894},[739],"",[572,897],{"className":898},[899],"fix",[572,901],{"className":902},[689,903],"nobreak",[572,905,712],{"className":906},[739],[572,908],{"className":909,"style":735},[689],[572,911,913,917,921,964,968,971],{"className":912},[625],[572,914],{"className":915,"style":916},[629],"height:0.7574em;vertical-align:-0.0833em;",[572,918,920],{"className":919},[642],"9",[572,922,924,928],{"className":923},[642],[572,925,927],{"className":926},[642],"0",[572,929,932],{"className":930},[931],"msupsub",[572,933,936],{"className":934},[935],"vlist-t",[572,937,940],{"className":938},[939],"vlist-r",[572,941,945],{"className":942,"style":944},[943],"vlist","height:0.6741em;",[572,946,948,953],{"style":947},"top:-3.063em;margin-right:0.05em;",[572,949],{"className":950,"style":952},[951],"pstrut","height:2.7em;",[572,954,960],{"className":955},[956,957,958,959],"sizing","reset-size6","size3","mtight",[572,961,828],{"className":962},[963,959],"mbin",[572,965],{"className":966,"style":967},[689],"margin-right:0.2222em;",[572,969,831],{"className":970},[963],[572,972],{"className":973,"style":967},[689],[572,975,977,981,985,988,991],{"className":976},[625],[572,978],{"className":979,"style":980},[629],"height:0.6944em;",[572,982,834],{"className":983,"style":984},[642,646],"margin-right:0.0315em;",[572,986],{"className":987,"style":967},[689],[572,989,837],{"className":990},[963],[572,992],{"className":993,"style":967},[689],[572,995,997,1000,1004],{"className":996},[625],[572,998],{"className":999,"style":944},[629],[572,1001,1003],{"className":1002},[642],"18",[572,1005,1007,1010],{"className":1006},[642],[572,1008,927],{"className":1009},[642],[572,1011,1013],{"className":1012},[931],[572,1014,1016],{"className":1015},[935],[572,1017,1019],{"className":1018},[939],[572,1020,1022],{"className":1021,"style":944},[943],[572,1023,1024,1027],{"style":947},[572,1025],{"className":1026,"style":952},[951],[572,1028,1030],{"className":1029},[956,957,958,959],[572,1031,828],{"className":1032},[963,959],".",[761,1035,1036,1037,1066,1067,1169,1170,1334,1335,1369,1370,1432,1433,1483],{},"Der Nenner darf nicht ",[572,1038,1040,1053],{"className":1039},[575],[572,1041,1043],{"className":1042},[579],[581,1044,1045],{"xmlns":583},[585,1046,1047,1051],{},[588,1048,1049],{},[603,1050,927],{},[613,1052,927],{"encoding":615},[572,1054,1056],{"className":1055,"ariaHidden":621},[620],[572,1057,1059,1063],{"className":1058},[625],[572,1060],{"className":1061,"style":1062},[629],"height:0.6444em;",[572,1064,927],{"className":1065},[642]," sein, also ",[572,1068,1070,1096],{"className":1069},[575],[572,1071,1073],{"className":1072},[579],[581,1074,1075],{"xmlns":583},[585,1076,1077,1093],{},[588,1078,1079,1081,1083,1085,1087,1090],{},[591,1080,593],{},[595,1082,597],{},[591,1084,608],{},[595,1086,819],{"mathvariant":818},[595,1088,1089],{},"±",[603,1091,1092],{},"1",[613,1094,1095],{"encoding":615},"\\tan x \\neq \\pm 1",[572,1097,1099,1156],{"className":1098,"ariaHidden":621},[620],[572,1100,1102,1105,1108,1111,1114,1117,1153],{"className":1101},[625],[572,1103],{"className":1104,"style":857},[629],[572,1106,593],{"className":1107},[634],[572,1109],{"className":1110,"style":690},[689],[572,1112,608],{"className":1113},[642,646],[572,1115],{"className":1116,"style":735},[689],[572,1118,1120,1147,1150],{"className":1119},[739],[572,1121,1123],{"className":1122},[739],[572,1124,1126],{"className":1125},[642,873],[572,1127,1129],{"className":1128},[877],[572,1130,1132,1135,1144],{"className":1131},[881],[572,1133],{"className":1134,"style":857},[629],[572,1136,1138],{"className":1137},[888],[572,1139,1141],{"className":1140},[642],[572,1142,895],{"className":1143},[739],[572,1145],{"className":1146},[899],[572,1148],{"className":1149},[689,903],[572,1151,712],{"className":1152},[739],[572,1154],{"className":1155,"style":735},[689],[572,1157,1159,1163,1166],{"className":1158},[625],[572,1160],{"className":1161,"style":1162},[629],"height:0.7278em;vertical-align:-0.0833em;",[572,1164,1089],{"className":1165},[642],[572,1167,1092],{"className":1168},[642],". Das schließt ",[572,1171,1173,1208],{"className":1172},[575],[572,1174,1176],{"className":1175},[579],[581,1177,1178],{"xmlns":583},[585,1179,1180,1205],{},[588,1181,1182,1184,1186,1193,1195,1197,1199],{},[591,1183,608],{},[595,1185,712],{},[821,1187,1188,1191],{},[603,1189,1190],{},"45",[595,1192,828],{},[595,1194,831],{},[591,1196,834],{},[595,1198,837],{},[821,1200,1201,1203],{},[603,1202,825],{},[595,1204,828],{},[613,1206,1207],{"encoding":615},"x = 45^\\circ + k \\cdot 90^\\circ",[572,1209,1211,1229,1278,1296],{"className":1210,"ariaHidden":621},[620],[572,1212,1214,1217,1220,1223,1226],{"className":1213},[625],[572,1215],{"className":1216,"style":749},[629],[572,1218,608],{"className":1219},[642,646],[572,1221],{"className":1222,"style":735},[689],[572,1224,712],{"className":1225},[739],[572,1227],{"className":1228,"style":735},[689],[572,1230,1232,1235,1239,1269,1272,1275],{"className":1231},[625],[572,1233],{"className":1234,"style":916},[629],[572,1236,1238],{"className":1237},[642],"4",[572,1240,1242,1246],{"className":1241},[642],[572,1243,1245],{"className":1244},[642],"5",[572,1247,1249],{"className":1248},[931],[572,1250,1252],{"className":1251},[935],[572,1253,1255],{"className":1254},[939],[572,1256,1258],{"className":1257,"style":944},[943],[572,1259,1260,1263],{"style":947},[572,1261],{"className":1262,"style":952},[951],[572,1264,1266],{"className":1265},[956,957,958,959],[572,1267,828],{"className":1268},[963,959],[572,1270],{"className":1271,"style":967},[689],[572,1273,831],{"className":1274},[963],[572,1276],{"className":1277,"style":967},[689],[572,1279,1281,1284,1287,1290,1293],{"className":1280},[625],[572,1282],{"className":1283,"style":980},[629],[572,1285,834],{"className":1286,"style":984},[642,646],[572,1288],{"className":1289,"style":967},[689],[572,1291,837],{"className":1292},[963],[572,1294],{"className":1295,"style":967},[689],[572,1297,1299,1302,1305],{"className":1298},[625],[572,1300],{"className":1301,"style":944},[629],[572,1303,920],{"className":1304},[642],[572,1306,1308,1311],{"className":1307},[642],[572,1309,927],{"className":1310},[642],[572,1312,1314],{"className":1313},[931],[572,1315,1317],{"className":1316},[935],[572,1318,1320],{"className":1319},[939],[572,1321,1323],{"className":1322,"style":944},[943],[572,1324,1325,1328],{"style":947},[572,1326],{"className":1327,"style":952},[951],[572,1329,1331],{"className":1330},[956,957,958,959],[572,1332,828],{"className":1333},[963,959]," aus; dort ist ",[572,1336,1338,1354],{"className":1337},[575],[572,1339,1341],{"className":1340},[579],[581,1342,1343],{"xmlns":583},[585,1344,1345,1351],{},[588,1346,1347,1349],{},[603,1348,605],{},[591,1350,608],{},[613,1352,1353],{"encoding":615},"2x",[572,1355,1357],{"className":1356,"ariaHidden":621},[620],[572,1358,1360,1363,1366],{"className":1359},[625],[572,1361],{"className":1362,"style":1062},[629],[572,1364,605],{"className":1365},[642],[572,1367,608],{"className":1368},[642,646]," eine Stelle wie ",[572,1371,1373,1391],{"className":1372},[575],[572,1374,1376],{"className":1375},[579],[581,1377,1378],{"xmlns":583},[585,1379,1380,1388],{},[588,1381,1382],{},[821,1383,1384,1386],{},[603,1385,825],{},[595,1387,828],{},[613,1389,1390],{"encoding":615},"90^\\circ",[572,1392,1394],{"className":1393,"ariaHidden":621},[620],[572,1395,1397,1400,1403],{"className":1396},[625],[572,1398],{"className":1399,"style":944},[629],[572,1401,920],{"className":1402},[642],[572,1404,1406,1409],{"className":1405},[642],[572,1407,927],{"className":1408},[642],[572,1410,1412],{"className":1411},[931],[572,1413,1415],{"className":1414},[935],[572,1416,1418],{"className":1417},[939],[572,1419,1421],{"className":1420,"style":944},[943],[572,1422,1423,1426],{"style":947},[572,1424],{"className":1425,"style":952},[951],[572,1427,1429],{"className":1428},[956,957,958,959],[572,1430,828],{"className":1431},[963,959],", an der ",[572,1434,1436,1459],{"className":1435},[575],[572,1437,1439],{"className":1438},[579],[581,1440,1441],{"xmlns":583},[585,1442,1443,1457],{},[588,1444,1445,1447,1449,1451,1453,1455],{},[591,1446,593],{},[595,1448,597],{},[595,1450,601],{"stretchy":600},[603,1452,605],{},[591,1454,608],{},[595,1456,611],{"stretchy":600},[613,1458,616],{"encoding":615},[572,1460,1462],{"className":1461,"ariaHidden":621},[620],[572,1463,1465,1468,1471,1474,1477,1480],{"className":1464},[625],[572,1466],{"className":1467,"style":630},[629],[572,1469,593],{"className":1470},[634],[572,1472,601],{"className":1473},[638],[572,1475,605],{"className":1476},[642],[572,1478,608],{"className":1479},[642,646],[572,1481,611],{"className":1482},[650]," nicht existiert.",[558,1485,1487],{"id":1486},"herleitung","Herleitung",[563,1489,1490,1491,1777,1778,1828],{},"Im Additionstheorem ",[572,1492,1494,1560],{"className":1493},[575],[572,1495,1497],{"className":1496},[579],[581,1498,1499],{"xmlns":583},[585,1500,1501,1557],{},[588,1502,1503,1505,1507,1509,1511,1513,1515,1517,1519],{},[591,1504,593],{},[595,1506,597],{},[595,1508,601],{"stretchy":600},[591,1510,608],{},[595,1512,831],{},[591,1514,709],{},[595,1516,611],{"stretchy":600},[595,1518,712],{},[1520,1521,1522,1538],"mfrac",{},[588,1523,1524,1526,1528,1530,1532,1534,1536],{},[591,1525,593],{},[595,1527,597],{},[591,1529,608],{},[595,1531,831],{},[591,1533,593],{},[595,1535,597],{},[591,1537,709],{},[588,1539,1540,1542,1545,1547,1549,1551,1553,1555],{},[603,1541,1092],{},[595,1543,1544],{},"−",[591,1546,593],{},[595,1548,597],{},[591,1550,608],{},[591,1552,593],{},[595,1554,597],{},[591,1556,709],{},[613,1558,1559],{"encoding":615},"\\tan(x + y) = \\frac{\\tan x + \\tan y}{1 - \\tan x \\tan y}",[572,1561,1563,1587,1608],{"className":1562,"ariaHidden":621},[620],[572,1564,1566,1569,1572,1575,1578,1581,1584],{"className":1565},[625],[572,1567],{"className":1568,"style":630},[629],[572,1570,593],{"className":1571},[634],[572,1573,601],{"className":1574},[638],[572,1576,608],{"className":1577},[642,646],[572,1579],{"className":1580,"style":967},[689],[572,1582,831],{"className":1583},[963],[572,1585],{"className":1586,"style":967},[689],[572,1588,1590,1593,1596,1599,1602,1605],{"className":1589},[625],[572,1591],{"className":1592,"style":630},[629],[572,1594,709],{"className":1595,"style":731},[642,646],[572,1597,611],{"className":1598},[650],[572,1600],{"className":1601,"style":735},[689],[572,1603,712],{"className":1604},[739],[572,1606],{"className":1607,"style":735},[689],[572,1609,1611,1615],{"className":1610},[625],[572,1612],{"className":1613,"style":1614},[629],"height:1.3578em;vertical-align:-0.4811em;",[572,1616,1618,1622,1774],{"className":1617},[642],[572,1619],{"className":1620},[638,1621],"nulldelimiter",[572,1623,1625],{"className":1624},[1520],[572,1626,1629,1765],{"className":1627},[935,1628],"vlist-t2",[572,1630,1632,1760],{"className":1631},[939],[572,1633,1636,1698,1709],{"className":1634,"style":1635},[943],"height:0.8767em;",[572,1637,1639,1643],{"style":1638},"top:-2.655em;",[572,1640],{"className":1641,"style":1642},[951],"height:3em;",[572,1644,1646],{"className":1645},[956,957,958,959],[572,1647,1649,1652,1655,1670,1674,1677,1680,1692,1695],{"className":1648},[642,959],[572,1650,1092],{"className":1651},[642,959],[572,1653,1544],{"className":1654},[963,959],[572,1656,1658,1662,1666],{"className":1657},[634,959],[572,1659,1661],{"className":1660},[959],"t",[572,1663,1665],{"className":1664},[959],"a",[572,1667,1669],{"className":1668},[959],"n",[572,1671],{"className":1672,"style":1673},[689,959],"margin-right:0.1952em;",[572,1675,608],{"className":1676},[642,646,959],[572,1678],{"className":1679,"style":1673},[689,959],[572,1681,1683,1686,1689],{"className":1682},[634,959],[572,1684,1661],{"className":1685},[959],[572,1687,1665],{"className":1688},[959],[572,1690,1669],{"className":1691},[959],[572,1693],{"className":1694,"style":1673},[689,959],[572,1696,709],{"className":1697,"style":731},[642,646,959],[572,1699,1701,1704],{"style":1700},"top:-3.23em;",[572,1702],{"className":1703,"style":1642},[951],[572,1705],{"className":1706,"style":1708},[1707],"frac-line","border-bottom-width:0.04em;",[572,1710,1712,1715],{"style":1711},"top:-3.4461em;",[572,1713],{"className":1714,"style":1642},[951],[572,1716,1718],{"className":1717},[956,957,958,959],[572,1719,1721,1733,1736,1739,1742,1754,1757],{"className":1720},[642,959],[572,1722,1724,1727,1730],{"className":1723},[634,959],[572,1725,1661],{"className":1726},[959],[572,1728,1665],{"className":1729},[959],[572,1731,1669],{"className":1732},[959],[572,1734],{"className":1735,"style":1673},[689,959],[572,1737,608],{"className":1738},[642,646,959],[572,1740,831],{"className":1741},[963,959],[572,1743,1745,1748,1751],{"className":1744},[634,959],[572,1746,1661],{"className":1747},[959],[572,1749,1665],{"className":1750},[959],[572,1752,1669],{"className":1753},[959],[572,1755],{"className":1756,"style":1673},[689,959],[572,1758,709],{"className":1759,"style":731},[642,646,959],[572,1761,1764],{"className":1762},[1763],"vlist-s","​",[572,1766,1768],{"className":1767},[939],[572,1769,1772],{"className":1770,"style":1771},[943],"height:0.4811em;",[572,1773],{},[572,1775],{"className":1776},[650,1621]," setzt man ",[572,1779,1781,1798],{"className":1780},[575],[572,1782,1784],{"className":1783},[579],[581,1785,1786],{"xmlns":583},[585,1787,1788,1796],{},[588,1789,1790,1792,1794],{},[591,1791,709],{},[595,1793,712],{},[591,1795,608],{},[613,1797,717],{"encoding":615},[572,1799,1801,1819],{"className":1800,"ariaHidden":621},[620],[572,1802,1804,1807,1810,1813,1816],{"className":1803},[625],[572,1805],{"className":1806,"style":727},[629],[572,1808,709],{"className":1809,"style":731},[642,646],[572,1811],{"className":1812,"style":735},[689],[572,1814,712],{"className":1815},[739],[572,1817],{"className":1818,"style":735},[689],[572,1820,1822,1825],{"className":1821},[625],[572,1823],{"className":1824,"style":749},[629],[572,1826,608],{"className":1827},[642,646],":",[572,1830,1833],{"className":1831},[1832],"katex-display",[572,1834,1836,1933],{"className":1835},[575],[572,1837,1839],{"className":1838},[579],[581,1840,1842],{"xmlns":583,"display":1841},"block",[585,1843,1844,1930],{},[588,1845,1846,1848,1850,1852,1854,1856,1858,1860,1898,1900],{},[591,1847,593],{},[595,1849,597],{},[595,1851,601],{"stretchy":600},[603,1853,605],{},[591,1855,608],{},[595,1857,611],{"stretchy":600},[595,1859,712],{},[1520,1861,1862,1878],{},[588,1863,1864,1866,1868,1870,1872,1874,1876],{},[591,1865,593],{},[595,1867,597],{},[591,1869,608],{},[595,1871,831],{},[591,1873,593],{},[595,1875,597],{},[591,1877,608],{},[588,1879,1880,1882,1884,1886,1888,1890,1892,1894,1896],{},[603,1881,1092],{},[595,1883,1544],{},[591,1885,593],{},[595,1887,597],{},[591,1889,608],{},[595,1891,837],{},[591,1893,593],{},[595,1895,597],{},[591,1897,608],{},[595,1899,712],{},[1520,1901,1902,1912],{},[588,1903,1904,1906,1908,1910],{},[603,1905,605],{},[591,1907,593],{},[595,1909,597],{},[591,1911,608],{},[588,1913,1914,1916,1918,1928],{},[603,1915,1092],{},[595,1917,1544],{},[821,1919,1920,1926],{},[588,1921,1922,1924],{},[591,1923,593],{},[595,1925,597],{},[603,1927,605],{},[591,1929,608],{},[613,1931,1932],{"encoding":615},"\\tan(2x) = \\frac{\\tan x + \\tan x}{1 - \\tan x \\cdot \\tan x} = \\frac{2 \\tan x}{1 - \\tan^2 x}",[572,1934,1936,1966,2108],{"className":1935,"ariaHidden":621},[620],[572,1937,1939,1942,1945,1948,1951,1954,1957,1960,1963],{"className":1938},[625],[572,1940],{"className":1941,"style":630},[629],[572,1943,593],{"className":1944},[634],[572,1946,601],{"className":1947},[638],[572,1949,605],{"className":1950},[642],[572,1952,608],{"className":1953},[642,646],[572,1955,611],{"className":1956},[650],[572,1958],{"className":1959,"style":735},[689],[572,1961,712],{"className":1962},[739],[572,1964],{"className":1965,"style":735},[689],[572,1967,1969,1973,2099,2102,2105],{"className":1968},[625],[572,1970],{"className":1971,"style":1972},[629],"height:2.0614em;vertical-align:-0.7693em;",[572,1974,1976,1979,2096],{"className":1975},[642],[572,1977],{"className":1978},[638,1621],[572,1980,1982],{"className":1981},[1520],[572,1983,1985,2087],{"className":1984},[935,1628],[572,1986,1988,2084],{"className":1987},[939],[572,1989,1992,2040,2048],{"className":1990,"style":1991},[943],"height:1.2921em;",[572,1993,1995,1998],{"style":1994},"top:-2.314em;",[572,1996],{"className":1997,"style":1642},[951],[572,1999,2001,2004,2007,2010,2013,2016,2019,2022,2025,2028,2031,2034,2037],{"className":2000},[642],[572,2002,1092],{"className":2003},[642],[572,2005],{"className":2006,"style":967},[689],[572,2008,1544],{"className":2009},[963],[572,2011],{"className":2012,"style":967},[689],[572,2014,593],{"className":2015},[634],[572,2017],{"className":2018,"style":690},[689],[572,2020,608],{"className":2021},[642,646],[572,2023],{"className":2024,"style":967},[689],[572,2026,837],{"className":2027},[963],[572,2029],{"className":2030,"style":967},[689],[572,2032,593],{"className":2033},[634],[572,2035],{"className":2036,"style":690},[689],[572,2038,608],{"className":2039},[642,646],[572,2041,2042,2045],{"style":1700},[572,2043],{"className":2044,"style":1642},[951],[572,2046],{"className":2047,"style":1708},[1707],[572,2049,2051,2054],{"style":2050},"top:-3.677em;",[572,2052],{"className":2053,"style":1642},[951],[572,2055,2057,2060,2063,2066,2069,2072,2075,2078,2081],{"className":2056},[642],[572,2058,593],{"className":2059},[634],[572,2061],{"className":2062,"style":690},[689],[572,2064,608],{"className":2065},[642,646],[572,2067],{"className":2068,"style":967},[689],[572,2070,831],{"className":2071},[963],[572,2073],{"className":2074,"style":967},[689],[572,2076,593],{"className":2077},[634],[572,2079],{"className":2080,"style":690},[689],[572,2082,608],{"className":2083},[642,646],[572,2085,1764],{"className":2086},[1763],[572,2088,2090],{"className":2089},[939],[572,2091,2094],{"className":2092,"style":2093},[943],"height:0.7693em;",[572,2095],{},[572,2097],{"className":2098},[650,1621],[572,2100],{"className":2101,"style":735},[689],[572,2103,712],{"className":2104},[739],[572,2106],{"className":2107,"style":735},[689],[572,2109,2111,2115],{"className":2110},[625],[572,2112],{"className":2113,"style":2114},[629],"height:2.1139em;vertical-align:-0.7924em;",[572,2116,2118,2121,2235],{"className":2117},[642],[572,2119],{"className":2120},[638,1621],[572,2122,2124],{"className":2123},[1520],[572,2125,2127,2226],{"className":2126},[935,1628],[572,2128,2130,2223],{"className":2129},[939],[572,2131,2134,2192,2200],{"className":2132,"style":2133},[943],"height:1.3214em;",[572,2135,2137,2140],{"style":2136},"top:-2.2909em;",[572,2138],{"className":2139,"style":1642},[951],[572,2141,2143,2146,2149,2152,2155,2186,2189],{"className":2142},[642],[572,2144,1092],{"className":2145},[642],[572,2147],{"className":2148,"style":967},[689],[572,2150,1544],{"className":2151},[963],[572,2153],{"className":2154,"style":967},[689],[572,2156,2158,2161],{"className":2157},[634],[572,2159,593],{"className":2160},[634],[572,2162,2164],{"className":2163},[931],[572,2165,2167],{"className":2166},[935],[572,2168,2170],{"className":2169},[939],[572,2171,2174],{"className":2172,"style":2173},[943],"height:0.8191em;",[572,2175,2177,2180],{"style":2176},"top:-3.068em;margin-right:0.05em;",[572,2178],{"className":2179,"style":952},[951],[572,2181,2183],{"className":2182},[956,957,958,959],[572,2184,605],{"className":2185},[642,959],[572,2187],{"className":2188,"style":690},[689],[572,2190,608],{"className":2191},[642,646],[572,2193,2194,2197],{"style":1700},[572,2195],{"className":2196,"style":1642},[951],[572,2198],{"className":2199,"style":1708},[1707],[572,2201,2202,2205],{"style":2050},[572,2203],{"className":2204,"style":1642},[951],[572,2206,2208,2211,2214,2217,2220],{"className":2207},[642],[572,2209,605],{"className":2210},[642],[572,2212],{"className":2213,"style":690},[689],[572,2215,593],{"className":2216},[634],[572,2218],{"className":2219,"style":690},[689],[572,2221,608],{"className":2222},[642,646],[572,2224,1764],{"className":2225},[1763],[572,2227,2229],{"className":2228},[939],[572,2230,2233],{"className":2231,"style":2232},[943],"height:0.7924em;",[572,2234],{},[572,2236],{"className":2237},[650,1621],[558,2239,2241],{"id":2240},"beispiele","Beispiele",[563,2243,2244,2245,1828],{},"Für einen Winkel mit ",[572,2246,2248,2271],{"className":2247},[575],[572,2249,2251],{"className":2250},[579],[581,2252,2253],{"xmlns":583},[585,2254,2255,2268],{},[588,2256,2257,2259,2261,2263,2265],{},[591,2258,593],{},[595,2260,597],{},[591,2262,608],{},[595,2264,712],{},[603,2266,2267],{},"0,5",[613,2269,2270],{"encoding":615},"\\tan x = 0{,}5",[572,2272,2274,2298],{"className":2273,"ariaHidden":621},[620],[572,2275,2277,2280,2283,2286,2289,2292,2295],{"className":2276},[625],[572,2278],{"className":2279,"style":682},[629],[572,2281,593],{"className":2282},[634],[572,2284],{"className":2285,"style":690},[689],[572,2287,608],{"className":2288},[642,646],[572,2290],{"className":2291,"style":735},[689],[572,2293,712],{"className":2294},[739],[572,2296],{"className":2297,"style":735},[689],[572,2299,2301,2305,2308,2316],{"className":2300},[625],[572,2302],{"className":2303,"style":2304},[629],"height:0.8389em;vertical-align:-0.1944em;",[572,2306,927],{"className":2307},[642],[572,2309,2311],{"className":2310},[642],[572,2312,2315],{"className":2313},[2314],"mpunct",",",[572,2317,1245],{"className":2318},[642],[572,2320,2322],{"className":2321},[1832],[572,2323,2325,2391],{"className":2324},[575],[572,2326,2328],{"className":2327},[579],[581,2329,2330],{"xmlns":583,"display":1841},[585,2331,2332,2388],{},[588,2333,2334,2336,2338,2340,2342,2344,2346,2348,2370,2372,2379,2381],{},[591,2335,593],{},[595,2337,597],{},[595,2339,601],{"stretchy":600},[603,2341,605],{},[591,2343,608],{},[595,2345,611],{"stretchy":600},[595,2347,712],{},[1520,2349,2350,2358],{},[588,2351,2352,2354,2356],{},[603,2353,605],{},[595,2355,837],{},[603,2357,2267],{},[588,2359,2360,2362,2364],{},[603,2361,1092],{},[595,2363,1544],{},[821,2365,2366,2368],{},[603,2367,2267],{},[603,2369,605],{},[595,2371,712],{},[1520,2373,2374,2376],{},[603,2375,1092],{},[603,2377,2378],{},"0,75",[595,2380,712],{},[1520,2382,2383,2385],{},[603,2384,1238],{},[603,2386,2387],{},"3",[613,2389,2390],{"encoding":615},"\\tan(2x) = \\frac{2 \\cdot 0{,}5}{1 - 0{,}5^2} = \\frac{1}{0{,}75} = \\frac{4}{3}",[572,2392,2394,2424,2573,2660],{"className":2393,"ariaHidden":621},[620],[572,2395,2397,2400,2403,2406,2409,2412,2415,2418,2421],{"className":2396},[625],[572,2398],{"className":2399,"style":630},[629],[572,2401,593],{"className":2402},[634],[572,2404,601],{"className":2405},[638],[572,2407,605],{"className":2408},[642],[572,2410,608],{"className":2411},[642,646],[572,2413,611],{"className":2414},[650],[572,2416],{"className":2417,"style":735},[689],[572,2419,712],{"className":2420},[739],[572,2422],{"className":2423,"style":735},[689],[572,2425,2427,2431,2564,2567,2570],{"className":2426},[625],[572,2428],{"className":2429,"style":2430},[629],"height:2.2019em;vertical-align:-0.8804em;",[572,2432,2434,2437,2561],{"className":2433},[642],[572,2435],{"className":2436},[638,1621],[572,2438,2440],{"className":2439},[1520],[572,2441,2443,2552],{"className":2442},[935,1628],[572,2444,2446,2549],{"className":2445},[939],[572,2447,2449,2509,2517],{"className":2448,"style":2133},[943],[572,2450,2451,2454],{"style":1994},[572,2452],{"className":2453,"style":1642},[951],[572,2455,2457,2460,2463,2466,2469,2472,2478],{"className":2456},[642],[572,2458,1092],{"className":2459},[642],[572,2461],{"className":2462,"style":967},[689],[572,2464,1544],{"className":2465},[963],[572,2467],{"className":2468,"style":967},[689],[572,2470,927],{"className":2471},[642],[572,2473,2475],{"className":2474},[642],[572,2476,2315],{"className":2477},[2314],[572,2479,2481,2484],{"className":2480},[642],[572,2482,1245],{"className":2483},[642],[572,2485,2487],{"className":2486},[931],[572,2488,2490],{"className":2489},[935],[572,2491,2493],{"className":2492},[939],[572,2494,2497],{"className":2495,"style":2496},[943],"height:0.7401em;",[572,2498,2500,2503],{"style":2499},"top:-2.989em;margin-right:0.05em;",[572,2501],{"className":2502,"style":952},[951],[572,2504,2506],{"className":2505},[956,957,958,959],[572,2507,605],{"className":2508},[642,959],[572,2510,2511,2514],{"style":1700},[572,2512],{"className":2513,"style":1642},[951],[572,2515],{"className":2516,"style":1708},[1707],[572,2518,2519,2522],{"style":2050},[572,2520],{"className":2521,"style":1642},[951],[572,2523,2525,2528,2531,2534,2537,2540,2546],{"className":2524},[642],[572,2526,605],{"className":2527},[642],[572,2529],{"className":2530,"style":967},[689],[572,2532,837],{"className":2533},[963],[572,2535],{"className":2536,"style":967},[689],[572,2538,927],{"className":2539},[642],[572,2541,2543],{"className":2542},[642],[572,2544,2315],{"className":2545},[2314],[572,2547,1245],{"className":2548},[642],[572,2550,1764],{"className":2551},[1763],[572,2553,2555],{"className":2554},[939],[572,2556,2559],{"className":2557,"style":2558},[943],"height:0.8804em;",[572,2560],{},[572,2562],{"className":2563},[650,1621],[572,2565],{"className":2566,"style":735},[689],[572,2568,712],{"className":2569},[739],[572,2571],{"className":2572,"style":735},[689],[572,2574,2576,2579,2651,2654,2657],{"className":2575},[625],[572,2577],{"className":2578,"style":2430},[629],[572,2580,2582,2585,2648],{"className":2581},[642],[572,2583],{"className":2584},[638,1621],[572,2586,2588],{"className":2587},[1520],[572,2589,2591,2640],{"className":2590},[935,1628],[572,2592,2594,2637],{"className":2593},[939],[572,2595,2597,2618,2626],{"className":2596,"style":2133},[943],[572,2598,2599,2602],{"style":1994},[572,2600],{"className":2601,"style":1642},[951],[572,2603,2605,2608,2614],{"className":2604},[642],[572,2606,927],{"className":2607},[642],[572,2609,2611],{"className":2610},[642],[572,2612,2315],{"className":2613},[2314],[572,2615,2617],{"className":2616},[642],"75",[572,2619,2620,2623],{"style":1700},[572,2621],{"className":2622,"style":1642},[951],[572,2624],{"className":2625,"style":1708},[1707],[572,2627,2628,2631],{"style":2050},[572,2629],{"className":2630,"style":1642},[951],[572,2632,2634],{"className":2633},[642],[572,2635,1092],{"className":2636},[642],[572,2638,1764],{"className":2639},[1763],[572,2641,2643],{"className":2642},[939],[572,2644,2646],{"className":2645,"style":2558},[943],[572,2647],{},[572,2649],{"className":2650},[650,1621],[572,2652],{"className":2653,"style":735},[689],[572,2655,712],{"className":2656},[739],[572,2658],{"className":2659,"style":735},[689],[572,2661,2663,2667],{"className":2662},[625],[572,2664],{"className":2665,"style":2666},[629],"height:2.0074em;vertical-align:-0.686em;",[572,2668,2670,2673,2727],{"className":2669},[642],[572,2671],{"className":2672},[638,1621],[572,2674,2676],{"className":2675},[1520],[572,2677,2679,2718],{"className":2678},[935,1628],[572,2680,2682,2715],{"className":2681},[939],[572,2683,2685,2696,2704],{"className":2684,"style":2133},[943],[572,2686,2687,2690],{"style":1994},[572,2688],{"className":2689,"style":1642},[951],[572,2691,2693],{"className":2692},[642],[572,2694,2387],{"className":2695},[642],[572,2697,2698,2701],{"style":1700},[572,2699],{"className":2700,"style":1642},[951],[572,2702],{"className":2703,"style":1708},[1707],[572,2705,2706,2709],{"style":2050},[572,2707],{"className":2708,"style":1642},[951],[572,2710,2712],{"className":2711},[642],[572,2713,1238],{"className":2714},[642],[572,2716,1764],{"className":2717},[1763],[572,2719,2721],{"className":2720},[939],[572,2722,2725],{"className":2723,"style":2724},[943],"height:0.686em;",[572,2726],{},[572,2728],{"className":2729},[650,1621],[563,2731,2732,2733,2818,2819,1828],{},"Mit ",[572,2734,2736,2759],{"className":2735},[575],[572,2737,2739],{"className":2738},[579],[581,2740,2741],{"xmlns":583},[585,2742,2743,2756],{},[588,2744,2745,2747,2749],{},[591,2746,608],{},[595,2748,712],{},[821,2750,2751,2754],{},[603,2752,2753],{},"30",[595,2755,828],{},[613,2757,2758],{"encoding":615},"x = 30^\\circ",[572,2760,2762,2780],{"className":2761,"ariaHidden":621},[620],[572,2763,2765,2768,2771,2774,2777],{"className":2764},[625],[572,2766],{"className":2767,"style":749},[629],[572,2769,608],{"className":2770},[642,646],[572,2772],{"className":2773,"style":735},[689],[572,2775,712],{"className":2776},[739],[572,2778],{"className":2779,"style":735},[689],[572,2781,2783,2786,2789],{"className":2782},[625],[572,2784],{"className":2785,"style":944},[629],[572,2787,2387],{"className":2788},[642],[572,2790,2792,2795],{"className":2791},[642],[572,2793,927],{"className":2794},[642],[572,2796,2798],{"className":2797},[931],[572,2799,2801],{"className":2800},[935],[572,2802,2804],{"className":2803},[939],[572,2805,2807],{"className":2806,"style":944},[943],[572,2808,2809,2812],{"style":947},[572,2810],{"className":2811,"style":952},[951],[572,2813,2815],{"className":2814},[956,957,958,959],[572,2816,828],{"className":2817},[963,959]," und ",[572,2820,2822,2855],{"className":2821},[575],[572,2823,2825],{"className":2824},[579],[581,2826,2827],{"xmlns":583},[585,2828,2829,2852],{},[588,2830,2831,2833,2835,2841,2843],{},[591,2832,593],{},[595,2834,597],{},[821,2836,2837,2839],{},[603,2838,2753],{},[595,2840,828],{},[595,2842,712],{},[1520,2844,2845,2847],{},[603,2846,1092],{},[2848,2849,2850],"msqrt",{},[603,2851,2387],{},[613,2853,2854],{"encoding":615},"\\tan 30^\\circ = \\frac{1}{\\sqrt{3}}",[572,2856,2858,2911],{"className":2857,"ariaHidden":621},[620],[572,2859,2861,2864,2867,2870,2873,2902,2905,2908],{"className":2860},[625],[572,2862],{"className":2863,"style":944},[629],[572,2865,593],{"className":2866},[634],[572,2868],{"className":2869,"style":690},[689],[572,2871,2387],{"className":2872},[642],[572,2874,2876,2879],{"className":2875},[642],[572,2877,927],{"className":2878},[642],[572,2880,2882],{"className":2881},[931],[572,2883,2885],{"className":2884},[935],[572,2886,2888],{"className":2887},[939],[572,2889,2891],{"className":2890,"style":944},[943],[572,2892,2893,2896],{"style":947},[572,2894],{"className":2895,"style":952},[951],[572,2897,2899],{"className":2898},[956,957,958,959],[572,2900,828],{"className":2901},[963,959],[572,2903],{"className":2904,"style":735},[689],[572,2906,712],{"className":2907},[739],[572,2909],{"className":2910,"style":735},[689],[572,2912,2914,2918],{"className":2913},[625],[572,2915],{"className":2916,"style":2917},[629],"height:1.3831em;vertical-align:-0.538em;",[572,2919,2921,2924,3048],{"className":2920},[642],[572,2922],{"className":2923},[638,1621],[572,2925,2927],{"className":2926},[1520],[572,2928,2930,3039],{"className":2929},[935,1628],[572,2931,2933,3036],{"className":2932},[939],[572,2934,2937,3013,3021],{"className":2935,"style":2936},[943],"height:0.8451em;",[572,2938,2940,2943],{"style":2939},"top:-2.551em;",[572,2941],{"className":2942,"style":1642},[951],[572,2944,2946],{"className":2945},[956,957,958,959],[572,2947,2949],{"className":2948},[642,959],[572,2950,2953],{"className":2951},[642,2952,959],"sqrt",[572,2954,2956,3004],{"className":2955},[935,1628],[572,2957,2959,3001],{"className":2958},[939],[572,2960,2963,2978],{"className":2961,"style":2962},[943],"height:0.9128em;",[572,2964,2968,2971],{"className":2965,"style":2967},[2966],"svg-align","top:-3em;",[572,2969],{"className":2970,"style":1642},[951],[572,2972,2975],{"className":2973,"style":2974},[642,959],"padding-left:0.833em;",[572,2976,2387],{"className":2977},[642,959],[572,2979,2981,2984],{"style":2980},"top:-2.8728em;",[572,2982],{"className":2983,"style":1642},[951],[572,2985,2989],{"className":2986,"style":2988},[2987,959],"hide-tail","min-width:0.853em;height:1.08em;",[2990,2991,2997],"svg",{"xmlns":2992,"width":2993,"height":2994,"viewBox":2995,"preserveAspectRatio":2996},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2998,2999],"path",{"d":3000},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[572,3002,1764],{"className":3003},[1763],[572,3005,3007],{"className":3006},[939],[572,3008,3011],{"className":3009,"style":3010},[943],"height:0.1272em;",[572,3012],{},[572,3014,3015,3018],{"style":1700},[572,3016],{"className":3017,"style":1642},[951],[572,3019],{"className":3020,"style":1708},[1707],[572,3022,3024,3027],{"style":3023},"top:-3.394em;",[572,3025],{"className":3026,"style":1642},[951],[572,3028,3030],{"className":3029},[956,957,958,959],[572,3031,3033],{"className":3032},[642,959],[572,3034,1092],{"className":3035},[642,959],[572,3037,1764],{"className":3038},[1763],[572,3040,3042],{"className":3041},[939],[572,3043,3046],{"className":3044,"style":3045},[943],"height:0.538em;",[572,3047],{},[572,3049],{"className":3050},[650,1621],[572,3052,3054],{"className":3053},[1832],[572,3055,3057,3128],{"className":3056},[575],[572,3058,3060],{"className":3059},[579],[581,3061,3062],{"xmlns":583,"display":1841},[585,3063,3064,3125],{},[588,3065,3066,3068,3070,3077,3079,3101,3103,3111,3113,3119,3121],{},[591,3067,593],{},[595,3069,597],{},[821,3071,3072,3075],{},[603,3073,3074],{},"60",[595,3076,828],{},[595,3078,712],{},[1520,3080,3081,3089],{},[1520,3082,3083,3085],{},[603,3084,605],{},[2848,3086,3087],{},[603,3088,2387],{},[588,3090,3091,3093,3095],{},[603,3092,1092],{},[595,3094,1544],{},[1520,3096,3097,3099],{},[603,3098,1092],{},[603,3100,2387],{},[595,3102,712],{},[1520,3104,3105,3107],{},[603,3106,605],{},[2848,3108,3109],{},[603,3110,2387],{},[595,3112,837],{},[1520,3114,3115,3117],{},[603,3116,2387],{},[603,3118,605],{},[595,3120,712],{},[2848,3122,3123],{},[603,3124,2387],{},[613,3126,3127],{"encoding":615},"\\tan 60^\\circ = \\frac{\\frac{2}{\\sqrt{3}}}{1 - \\frac{1}{3}} = \\frac{2}{\\sqrt{3}} \\cdot \\frac{3}{2} = \\sqrt{3}",[572,3129,3131,3187,3456,3583,3660],{"className":3130,"ariaHidden":621},[620],[572,3132,3134,3138,3141,3144,3148,3178,3181,3184],{"className":3133},[625],[572,3135],{"className":3136,"style":3137},[629],"height:0.7241em;",[572,3139,593],{"className":3140},[634],[572,3142],{"className":3143,"style":690},[689],[572,3145,3147],{"className":3146},[642],"6",[572,3149,3151,3154],{"className":3150},[642],[572,3152,927],{"className":3153},[642],[572,3155,3157],{"className":3156},[931],[572,3158,3160],{"className":3159},[935],[572,3161,3163],{"className":3162},[939],[572,3164,3166],{"className":3165,"style":3137},[943],[572,3167,3169,3172],{"style":3168},"top:-3.113em;margin-right:0.05em;",[572,3170],{"className":3171,"style":952},[951],[572,3173,3175],{"className":3174},[956,957,958,959],[572,3176,828],{"className":3177},[963,959],[572,3179],{"className":3180,"style":735},[689],[572,3182,712],{"className":3183},[739],[572,3185],{"className":3186,"style":735},[689],[572,3188,3190,3194,3447,3450,3453],{"className":3189},[625],[572,3191],{"className":3192,"style":3193},[629],"height:2.8532em;vertical-align:-1.0801em;",[572,3195,3197,3200,3444],{"className":3196},[642],[572,3198],{"className":3199},[638,1621],[572,3201,3203],{"className":3202},[1520],[572,3204,3206,3435],{"className":3205},[935,1628],[572,3207,3209,3432],{"className":3208},[939],[572,3210,3213,3303,3311],{"className":3211,"style":3212},[943],"height:1.7731em;",[572,3214,3216,3219],{"style":3215},"top:-2.2649em;",[572,3217],{"className":3218,"style":1642},[951],[572,3220,3222,3225,3228,3231,3234],{"className":3221},[642],[572,3223,1092],{"className":3224},[642],[572,3226],{"className":3227,"style":967},[689],[572,3229,1544],{"className":3230},[963],[572,3232],{"className":3233,"style":967},[689],[572,3235,3237,3240,3300],{"className":3236},[642],[572,3238],{"className":3239},[638,1621],[572,3241,3243],{"className":3242},[1520],[572,3244,3246,3291],{"className":3245},[935,1628],[572,3247,3249,3288],{"className":3248},[939],[572,3250,3252,3266,3274],{"className":3251,"style":2936},[943],[572,3253,3254,3257],{"style":1638},[572,3255],{"className":3256,"style":1642},[951],[572,3258,3260],{"className":3259},[956,957,958,959],[572,3261,3263],{"className":3262},[642,959],[572,3264,2387],{"className":3265},[642,959],[572,3267,3268,3271],{"style":1700},[572,3269],{"className":3270,"style":1642},[951],[572,3272],{"className":3273,"style":1708},[1707],[572,3275,3276,3279],{"style":3023},[572,3277],{"className":3278,"style":1642},[951],[572,3280,3282],{"className":3281},[956,957,958,959],[572,3283,3285],{"className":3284},[642,959],[572,3286,1092],{"className":3287},[642,959],[572,3289,1764],{"className":3290},[1763],[572,3292,3294],{"className":3293},[939],[572,3295,3298],{"className":3296,"style":3297},[943],"height:0.345em;",[572,3299],{},[572,3301],{"className":3302},[650,1621],[572,3304,3305,3308],{"style":1700},[572,3306],{"className":3307,"style":1642},[951],[572,3309],{"className":3310,"style":1708},[1707],[572,3312,3314,3317],{"style":3313},"top:-3.928em;",[572,3315],{"className":3316,"style":1642},[951],[572,3318,3320],{"className":3319},[642],[572,3321,3323,3326,3429],{"className":3322},[642],[572,3324],{"className":3325},[638,1621],[572,3327,3329],{"className":3328},[1520],[572,3330,3332,3421],{"className":3331},[935,1628],[572,3333,3335,3418],{"className":3334},[939],[572,3336,3338,3396,3404],{"className":3337,"style":2936},[943],[572,3339,3340,3343],{"style":2939},[572,3341],{"className":3342,"style":1642},[951],[572,3344,3346],{"className":3345},[956,957,958,959],[572,3347,3349],{"className":3348},[642,959],[572,3350,3352],{"className":3351},[642,2952,959],[572,3353,3355,3388],{"className":3354},[935,1628],[572,3356,3358,3385],{"className":3357},[939],[572,3359,3361,3373],{"className":3360,"style":2962},[943],[572,3362,3364,3367],{"className":3363,"style":2967},[2966],[572,3365],{"className":3366,"style":1642},[951],[572,3368,3370],{"className":3369,"style":2974},[642,959],[572,3371,2387],{"className":3372},[642,959],[572,3374,3375,3378],{"style":2980},[572,3376],{"className":3377,"style":1642},[951],[572,3379,3381],{"className":3380,"style":2988},[2987,959],[2990,3382,3383],{"xmlns":2992,"width":2993,"height":2994,"viewBox":2995,"preserveAspectRatio":2996},[2998,3384],{"d":3000},[572,3386,1764],{"className":3387},[1763],[572,3389,3391],{"className":3390},[939],[572,3392,3394],{"className":3393,"style":3010},[943],[572,3395],{},[572,3397,3398,3401],{"style":1700},[572,3399],{"className":3400,"style":1642},[951],[572,3402],{"className":3403,"style":1708},[1707],[572,3405,3406,3409],{"style":3023},[572,3407],{"className":3408,"style":1642},[951],[572,3410,3412],{"className":3411},[956,957,958,959],[572,3413,3415],{"className":3414},[642,959],[572,3416,605],{"className":3417},[642,959],[572,3419,1764],{"className":3420},[1763],[572,3422,3424],{"className":3423},[939],[572,3425,3427],{"className":3426,"style":3045},[943],[572,3428],{},[572,3430],{"className":3431},[650,1621],[572,3433,1764],{"className":3434},[1763],[572,3436,3438],{"className":3437},[939],[572,3439,3442],{"className":3440,"style":3441},[943],"height:1.0801em;",[572,3443],{},[572,3445],{"className":3446},[650,1621],[572,3448],{"className":3449,"style":735},[689],[572,3451,712],{"className":3452},[739],[572,3454],{"className":3455,"style":735},[689],[572,3457,3459,3463,3574,3577,3580],{"className":3458},[625],[572,3460],{"className":3461,"style":3462},[629],"height:2.2514em;vertical-align:-0.93em;",[572,3464,3466,3469,3571],{"className":3465},[642],[572,3467],{"className":3468},[638,1621],[572,3470,3472],{"className":3471},[1520],[572,3473,3475,3562],{"className":3474},[935,1628],[572,3476,3478,3559],{"className":3477},[939],[572,3479,3481,3540,3548],{"className":3480,"style":2133},[943],[572,3482,3484,3487],{"style":3483},"top:-2.2028em;",[572,3485],{"className":3486,"style":1642},[951],[572,3488,3490],{"className":3489},[642],[572,3491,3493],{"className":3492},[642,2952],[572,3494,3496,3531],{"className":3495},[935,1628],[572,3497,3499,3528],{"className":3498},[939],[572,3500,3503,3515],{"className":3501,"style":3502},[943],"height:0.9072em;",[572,3504,3506,3509],{"className":3505,"style":2967},[2966],[572,3507],{"className":3508,"style":1642},[951],[572,3510,3512],{"className":3511,"style":2974},[642],[572,3513,2387],{"className":3514},[642],[572,3516,3518,3521],{"style":3517},"top:-2.8672em;",[572,3519],{"className":3520,"style":1642},[951],[572,3522,3524],{"className":3523,"style":2988},[2987],[2990,3525,3526],{"xmlns":2992,"width":2993,"height":2994,"viewBox":2995,"preserveAspectRatio":2996},[2998,3527],{"d":3000},[572,3529,1764],{"className":3530},[1763],[572,3532,3534],{"className":3533},[939],[572,3535,3538],{"className":3536,"style":3537},[943],"height:0.1328em;",[572,3539],{},[572,3541,3542,3545],{"style":1700},[572,3543],{"className":3544,"style":1642},[951],[572,3546],{"className":3547,"style":1708},[1707],[572,3549,3550,3553],{"style":2050},[572,3551],{"className":3552,"style":1642},[951],[572,3554,3556],{"className":3555},[642],[572,3557,605],{"className":3558},[642],[572,3560,1764],{"className":3561},[1763],[572,3563,3565],{"className":3564},[939],[572,3566,3569],{"className":3567,"style":3568},[943],"height:0.93em;",[572,3570],{},[572,3572],{"className":3573},[650,1621],[572,3575],{"className":3576,"style":967},[689],[572,3578,837],{"className":3579},[963],[572,3581],{"className":3582,"style":967},[689],[572,3584,3586,3589,3651,3654,3657],{"className":3585},[625],[572,3587],{"className":3588,"style":2666},[629],[572,3590,3592,3595,3648],{"className":3591},[642],[572,3593],{"className":3594},[638,1621],[572,3596,3598],{"className":3597},[1520],[572,3599,3601,3640],{"className":3600},[935,1628],[572,3602,3604,3637],{"className":3603},[939],[572,3605,3607,3618,3626],{"className":3606,"style":2133},[943],[572,3608,3609,3612],{"style":1994},[572,3610],{"className":3611,"style":1642},[951],[572,3613,3615],{"className":3614},[642],[572,3616,605],{"className":3617},[642],[572,3619,3620,3623],{"style":1700},[572,3621],{"className":3622,"style":1642},[951],[572,3624],{"className":3625,"style":1708},[1707],[572,3627,3628,3631],{"style":2050},[572,3629],{"className":3630,"style":1642},[951],[572,3632,3634],{"className":3633},[642],[572,3635,2387],{"className":3636},[642],[572,3638,1764],{"className":3639},[1763],[572,3641,3643],{"className":3642},[939],[572,3644,3646],{"className":3645,"style":2724},[943],[572,3647],{},[572,3649],{"className":3650},[650,1621],[572,3652],{"className":3653,"style":735},[689],[572,3655,712],{"className":3656},[739],[572,3658],{"className":3659,"style":735},[689],[572,3661,3663,3667],{"className":3662},[625],[572,3664],{"className":3665,"style":3666},[629],"height:1.04em;vertical-align:-0.0839em;",[572,3668,3670],{"className":3669},[642,2952],[572,3671,3673,3708],{"className":3672},[935,1628],[572,3674,3676,3705],{"className":3675},[939],[572,3677,3680,3692],{"className":3678,"style":3679},[943],"height:0.9561em;",[572,3681,3683,3686],{"className":3682,"style":2967},[2966],[572,3684],{"className":3685,"style":1642},[951],[572,3687,3689],{"className":3688,"style":2974},[642],[572,3690,2387],{"className":3691},[642],[572,3693,3695,3698],{"style":3694},"top:-2.9161em;",[572,3696],{"className":3697,"style":1642},[951],[572,3699,3701],{"className":3700,"style":2988},[2987],[2990,3702,3703],{"xmlns":2992,"width":2993,"height":2994,"viewBox":2995,"preserveAspectRatio":2996},[2998,3704],{"d":3000},[572,3706,1764],{"className":3707},[1763],[572,3709,3711],{"className":3710},[939],[572,3712,3715],{"className":3713,"style":3714},[943],"height:0.0839em;",[572,3716],{},[558,3718,3720],{"id":3719},"typische-fehler","Typische Fehler",[758,3722,3723,4132,4229],{},[761,3724,3725,3816,3817,3900,3901,3957,3958,1033],{},[572,3726,3728,3762],{"className":3727},[575],[572,3729,3731],{"className":3730},[579],[581,3732,3733],{"xmlns":583},[585,3734,3735,3759],{},[588,3736,3737,3739,3741,3743,3745,3747,3749,3751,3753,3755,3757],{},[591,3738,593],{},[595,3740,597],{},[595,3742,601],{"stretchy":600},[603,3744,605],{},[591,3746,608],{},[595,3748,611],{"stretchy":600},[595,3750,712],{},[603,3752,605],{},[591,3754,593],{},[595,3756,597],{},[591,3758,608],{},[613,3760,3761],{"encoding":615},"\\tan(2x) = 2 \\tan x",[572,3763,3765,3795],{"className":3764,"ariaHidden":621},[620],[572,3766,3768,3771,3774,3777,3780,3783,3786,3789,3792],{"className":3767},[625],[572,3769],{"className":3770,"style":630},[629],[572,3772,593],{"className":3773},[634],[572,3775,601],{"className":3776},[638],[572,3778,605],{"className":3779},[642],[572,3781,608],{"className":3782},[642,646],[572,3784,611],{"className":3785},[650],[572,3787],{"className":3788,"style":735},[689],[572,3790,712],{"className":3791},[739],[572,3793],{"className":3794,"style":735},[689],[572,3796,3798,3801,3804,3807,3810,3813],{"className":3797},[625],[572,3799],{"className":3800,"style":1062},[629],[572,3802,605],{"className":3803},[642],[572,3805],{"className":3806,"style":690},[689],[572,3808,593],{"className":3809},[634],[572,3811],{"className":3812,"style":690},[689],[572,3814,608],{"className":3815},[642,646]," annehmen. Bei ",[572,3818,3820,3841],{"className":3819},[575],[572,3821,3823],{"className":3822},[579],[581,3824,3825],{"xmlns":583},[585,3826,3827,3839],{},[588,3828,3829,3831,3833],{},[591,3830,608],{},[595,3832,712],{},[821,3834,3835,3837],{},[603,3836,2753],{},[595,3838,828],{},[613,3840,2758],{"encoding":615},[572,3842,3844,3862],{"className":3843,"ariaHidden":621},[620],[572,3845,3847,3850,3853,3856,3859],{"className":3846},[625],[572,3848],{"className":3849,"style":749},[629],[572,3851,608],{"className":3852},[642,646],[572,3854],{"className":3855,"style":735},[689],[572,3857,712],{"className":3858},[739],[572,3860],{"className":3861,"style":735},[689],[572,3863,3865,3868,3871],{"className":3864},[625],[572,3866],{"className":3867,"style":944},[629],[572,3869,2387],{"className":3870},[642],[572,3872,3874,3877],{"className":3873},[642],[572,3875,927],{"className":3876},[642],[572,3878,3880],{"className":3879},[931],[572,3881,3883],{"className":3882},[935],[572,3884,3886],{"className":3885},[939],[572,3887,3889],{"className":3888,"style":944},[943],[572,3890,3891,3894],{"style":947},[572,3892],{"className":3893,"style":952},[951],[572,3895,3897],{"className":3896},[956,957,958,959],[572,3898,828],{"className":3899},[963,959]," wäre das ",[572,3902,3904,3922],{"className":3903},[575],[572,3905,3907],{"className":3906},[579],[581,3908,3909],{"xmlns":583},[585,3910,3911,3919],{},[588,3912,3913,3916],{},[595,3914,3915],{},"≈",[603,3917,3918],{},"1,155",[613,3920,3921],{"encoding":615},"\\approx 1{,}155",[572,3923,3925,3938],{"className":3924,"ariaHidden":621},[620],[572,3926,3928,3932,3935],{"className":3927},[625],[572,3929],{"className":3930,"style":3931},[629],"height:0.4831em;",[572,3933,3915],{"className":3934},[739],[572,3936],{"className":3937,"style":735},[689],[572,3939,3941,3944,3947,3953],{"className":3940},[625],[572,3942],{"className":3943,"style":2304},[629],[572,3945,1092],{"className":3946},[642],[572,3948,3950],{"className":3949},[642],[572,3951,2315],{"className":3952},[2314],[572,3954,3956],{"className":3955},[642],"155",", richtig ist ",[572,3959,3961,3994],{"className":3960},[575],[572,3962,3964],{"className":3963},[579],[581,3965,3966],{"xmlns":583},[585,3967,3968,3991],{},[588,3969,3970,3972,3974,3980,3982,3986,3988],{},[591,3971,593],{},[595,3973,597],{},[821,3975,3976,3978],{},[603,3977,3074],{},[595,3979,828],{},[595,3981,712],{},[2848,3983,3984],{},[603,3985,2387],{},[595,3987,3915],{},[603,3989,3990],{},"1,732",[613,3992,3993],{"encoding":615},"\\tan 60^\\circ = \\sqrt{3} \\approx 1{,}732",[572,3995,3997,4050,4113],{"className":3996,"ariaHidden":621},[620],[572,3998,4000,4003,4006,4009,4012,4041,4044,4047],{"className":3999},[625],[572,4001],{"className":4002,"style":944},[629],[572,4004,593],{"className":4005},[634],[572,4007],{"className":4008,"style":690},[689],[572,4010,3147],{"className":4011},[642],[572,4013,4015,4018],{"className":4014},[642],[572,4016,927],{"className":4017},[642],[572,4019,4021],{"className":4020},[931],[572,4022,4024],{"className":4023},[935],[572,4025,4027],{"className":4026},[939],[572,4028,4030],{"className":4029,"style":944},[943],[572,4031,4032,4035],{"style":947},[572,4033],{"className":4034,"style":952},[951],[572,4036,4038],{"className":4037},[956,957,958,959],[572,4039,828],{"className":4040},[963,959],[572,4042],{"className":4043,"style":735},[689],[572,4045,712],{"className":4046},[739],[572,4048],{"className":4049,"style":735},[689],[572,4051,4053,4057,4104,4107,4110],{"className":4052},[625],[572,4054],{"className":4055,"style":4056},[629],"height:1.04em;vertical-align:-0.1328em;",[572,4058,4060],{"className":4059},[642,2952],[572,4061,4063,4096],{"className":4062},[935,1628],[572,4064,4066,4093],{"className":4065},[939],[572,4067,4069,4081],{"className":4068,"style":3502},[943],[572,4070,4072,4075],{"className":4071,"style":2967},[2966],[572,4073],{"className":4074,"style":1642},[951],[572,4076,4078],{"className":4077,"style":2974},[642],[572,4079,2387],{"className":4080},[642],[572,4082,4083,4086],{"style":3517},[572,4084],{"className":4085,"style":1642},[951],[572,4087,4089],{"className":4088,"style":2988},[2987],[2990,4090,4091],{"xmlns":2992,"width":2993,"height":2994,"viewBox":2995,"preserveAspectRatio":2996},[2998,4092],{"d":3000},[572,4094,1764],{"className":4095},[1763],[572,4097,4099],{"className":4098},[939],[572,4100,4102],{"className":4101,"style":3537},[943],[572,4103],{},[572,4105],{"className":4106,"style":735},[689],[572,4108,3915],{"className":4109},[739],[572,4111],{"className":4112,"style":735},[689],[572,4114,4116,4119,4122,4128],{"className":4115},[625],[572,4117],{"className":4118,"style":2304},[629],[572,4120,1092],{"className":4121},[642],[572,4123,4125],{"className":4124},[642],[572,4126,2315],{"className":4127},[2314],[572,4129,4131],{"className":4130},[642],"732",[761,4133,4134,4135,4228],{},"Im Nenner ",[572,4136,4138,4166],{"className":4137},[575],[572,4139,4141],{"className":4140},[579],[581,4142,4143],{"xmlns":583},[585,4144,4145,4163],{},[588,4146,4147,4149,4151,4161],{},[603,4148,1092],{},[595,4150,831],{},[821,4152,4153,4159],{},[588,4154,4155,4157],{},[591,4156,593],{},[595,4158,597],{},[603,4160,605],{},[591,4162,608],{},[613,4164,4165],{"encoding":615},"1 + \\tan^2 x",[572,4167,4169,4187],{"className":4168,"ariaHidden":621},[620],[572,4170,4172,4175,4178,4181,4184],{"className":4171},[625],[572,4173],{"className":4174,"style":1162},[629],[572,4176,1092],{"className":4177},[642],[572,4179],{"className":4180,"style":967},[689],[572,4182,831],{"className":4183},[963],[572,4185],{"className":4186,"style":967},[689],[572,4188,4190,4193,4222,4225],{"className":4189},[625],[572,4191],{"className":4192,"style":2173},[629],[572,4194,4196,4199],{"className":4195},[634],[572,4197,593],{"className":4198},[634],[572,4200,4202],{"className":4201},[931],[572,4203,4205],{"className":4204},[935],[572,4206,4208],{"className":4207},[939],[572,4209,4211],{"className":4210,"style":2173},[943],[572,4212,4213,4216],{"style":2176},[572,4214],{"className":4215,"style":952},[951],[572,4217,4219],{"className":4218},[956,957,958,959],[572,4220,605],{"className":4221},[642,959],[572,4223],{"className":4224,"style":690},[689],[572,4226,608],{"className":4227},[642,646]," schreiben. Bei der Summe steht im Nenner ein Minus.",[761,4230,4231,4302,4303,4381,4382,1033],{},[572,4232,4234,4258],{"className":4233},[575],[572,4235,4237],{"className":4236},[579],[581,4238,4239],{"xmlns":583},[585,4240,4241,4255],{},[588,4242,4243,4253],{},[821,4244,4245,4251],{},[588,4246,4247,4249],{},[591,4248,593],{},[595,4250,597],{},[603,4252,605],{},[591,4254,608],{},[613,4256,4257],{"encoding":615},"\\tan^2 x",[572,4259,4261],{"className":4260,"ariaHidden":621},[620],[572,4262,4264,4267,4296,4299],{"className":4263},[625],[572,4265],{"className":4266,"style":2173},[629],[572,4268,4270,4273],{"className":4269},[634],[572,4271,593],{"className":4272},[634],[572,4274,4276],{"className":4275},[931],[572,4277,4279],{"className":4278},[935],[572,4280,4282],{"className":4281},[939],[572,4283,4285],{"className":4284,"style":2173},[943],[572,4286,4287,4290],{"style":2176},[572,4288],{"className":4289,"style":952},[951],[572,4291,4293],{"className":4292},[956,957,958,959],[572,4294,605],{"className":4295},[642,959],[572,4297],{"className":4298,"style":690},[689],[572,4300,608],{"className":4301},[642,646]," als ",[572,4304,4306,4332],{"className":4305},[575],[572,4307,4309],{"className":4308},[579],[581,4310,4311],{"xmlns":583},[585,4312,4313,4329],{},[588,4314,4315,4317,4319,4321,4327],{},[591,4316,593],{},[595,4318,597],{},[595,4320,601],{"stretchy":600},[821,4322,4323,4325],{},[591,4324,608],{},[603,4326,605],{},[595,4328,611],{"stretchy":600},[613,4330,4331],{"encoding":615},"\\tan(x^2)",[572,4333,4335],{"className":4334,"ariaHidden":621},[620],[572,4336,4338,4342,4345,4348,4378],{"className":4337},[625],[572,4339],{"className":4340,"style":4341},[629],"height:1.0641em;vertical-align:-0.25em;",[572,4343,593],{"className":4344},[634],[572,4346,601],{"className":4347},[638],[572,4349,4351,4354],{"className":4350},[642],[572,4352,608],{"className":4353},[642,646],[572,4355,4357],{"className":4356},[931],[572,4358,4360],{"className":4359},[935],[572,4361,4363],{"className":4362},[939],[572,4364,4367],{"className":4365,"style":4366},[943],"height:0.8141em;",[572,4368,4369,4372],{"style":947},[572,4370],{"className":4371,"style":952},[951],[572,4373,4375],{"className":4374},[956,957,958,959],[572,4376,605],{"className":4377},[642,959],[572,4379,611],{"className":4380},[650]," lesen. Gemeint ist ",[572,4383,4385,4411],{"className":4384},[575],[572,4386,4388],{"className":4387},[579],[581,4389,4390],{"xmlns":583},[585,4391,4392,4408],{},[588,4393,4394,4396,4398,4400,4402],{},[595,4395,601],{"stretchy":600},[591,4397,593],{},[595,4399,597],{},[591,4401,608],{},[821,4403,4404,4406],{},[595,4405,611],{"stretchy":600},[603,4407,605],{},[613,4409,4410],{"encoding":615},"(\\tan x)^2",[572,4412,4414],{"className":4413,"ariaHidden":621},[620],[572,4415,4417,4420,4423,4426,4429,4432],{"className":4416},[625],[572,4418],{"className":4419,"style":4341},[629],[572,4421,601],{"className":4422},[638],[572,4424,593],{"className":4425},[634],[572,4427],{"className":4428,"style":690},[689],[572,4430,608],{"className":4431},[642,646],[572,4433,4435,4438],{"className":4434},[650],[572,4436,611],{"className":4437},[650],[572,4439,4441],{"className":4440},[931],[572,4442,4444],{"className":4443},[935],[572,4445,4447],{"className":4446},[939],[572,4448,4450],{"className":4449,"style":4366},[943],[572,4451,4452,4455],{"style":947},[572,4453],{"className":4454,"style":952},[951],[572,4456,4458],{"className":4457},[956,957,958,959],[572,4459,605],{"className":4460},[642,959],{"title":4462,"searchDepth":4463,"depth":4463,"links":4464},"",2,[4465,4466,4467,4468],{"id":560,"depth":4463,"text":561},{"id":1486,"depth":4463,"text":1487},{"id":2240,"depth":4463,"text":2241},{"id":3719,"depth":4463,"text":3720},[4470,4475,4478,4480,4484,4487,4489,4492,4494,4497],{"lhs":4471,"rhs":4472,"where":4473},"tan(2*x)","2*tan(x)\u002F(1 - tan(x)^2)",{"x":4474},0.3,{"lhs":4471,"rhs":4472,"where":4476},{"x":4477},2.2,{"lhs":4479,"rhs":4472},"(tan(x) + tan(x))\u002F(1 - tan(x)*tan(x))",{"lhs":4481,"rhs":4472,"where":4482},"(2*sin(x)*cos(x))\u002F(cos(x)^2 - sin(x)^2)",{"x":4483},1.1,{"lhs":4485,"rhs":4486},"2*0.5\u002F(1 - 0.5^2)","4\u002F3",{"lhs":4488,"rhs":4486},"tan(2*atan(0.5))",{"lhs":4490,"rhs":4491},"2*(1\u002Fsqrt(3))\u002F(1 - (1\u002Fsqrt(3))^2)","sqrt(3)",{"lhs":4493,"rhs":4491},"tan(60*pi\u002F180)",{"lhs":4495,"rhs":4496},"round(2*tan(30*pi\u002F180), 3)","1.155",{"lhs":4498,"rhs":4499},"round(sqrt(3), 3)","1.732","x \\neq \\frac{\\pi}{2} + k\\pi,\\ x \\neq \\frac{\\pi}{4} + k \\cdot \\frac{\\pi}{2},\\ k \\in \\mathbb{Z}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>π\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\neq \\frac{\\pi}{2} + k\\pi,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0404em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6954em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmn>4\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\neq \\frac{\\pi}{4} + k \\cdot \\frac{\\pi}{2},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0404em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6954em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">4\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0404em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6954em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">Z\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\mathbb{Z}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">Z\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","tangent-double-angle","\\tan(2x) = \\frac{2 \\tan x}{1 - \\tan^2 x}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\tan(2x) = \\frac{2 \\tan x}{1 - \\tan^2 x}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">tan\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.1139em;vertical-align:-0.7924em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.2909em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop\">tan\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8191em;\">\u003Cspan style=\"top:-3.068em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">tan\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7924em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-tangens",[],[4513,4514,4515,4516],"tangent-addition","sine-double-angle","cosine-double-angle","tangent-quotient",{"title":548,"description":4462},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-tangens","Der Tangens des doppelten Winkels lässt sich aus dem Tangens des einfachen Winkels berechnen.",[4521,4522,4523,4524],"doppelwinkel","tangens","additionstheorem","identität",[4526,4529],{"symbol":608,"meaning":4527,"symbolHtml":4528},"Winkel, für den tan x und tan(2x) definiert sind","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":834,"meaning":4530,"symbolHtml":4531},"beliebige ganze Zahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Dgn5qnI84ziBsHnUYOtJO6orSpGdic7B9Zdk0_bXFc0",[4534,4537,4540,4543],{"stem":4535,"title":4536,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fadditionstheorem-tangens","Additionstheorem für den Tangens",{"stem":4538,"title":4539,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-kosinus","Doppelwinkelformel für den Kosinus",{"stem":4541,"title":4542,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-sinus","Doppelwinkelformel für den Sinus",{"stem":4544,"title":4545,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftangens-als-quotient","Tangens als Quotient von Sinus und Kosinus",1793824262020]