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x",[573,1130,1132,1151],{"className":1131,"ariaHidden":603},[602],[573,1133,1135,1139,1142,1145,1148],{"className":1134},[607],[573,1136],{"className":1137,"style":1138},[611],"height:0.625em;vertical-align:-0.1944em;",[573,1140,958],{"className":1141,"style":1030},[616,617],[573,1143],{"className":1144,"style":698},[697],[573,1146,656],{"className":1147},[702],[573,1149],{"className":1150,"style":698},[697],[573,1152,1154,1157],{"className":1153},[607],[573,1155],{"className":1156,"style":612},[611],[573,1158,594],{"className":1159},[616,617],":",[573,1162,1165],{"className":1163},[1164],"katex-display",[573,1166,1168,1237],{"className":1167},[576],[573,1169,1171],{"className":1170},[580],[582,1172,1174],{"xmlns":584,"display":1173},"block",[586,1175,1176,1234],{},[589,1177,1178,1180,1182,1184,1186,1188,1190,1192,1194,1196,1198,1200,1202,1204,1206,1208,1210,1212,1214,1216,1218,1220,1222,1224,1226,1228,1230,1232],{},[592,1179,636],{},[638,1181,640],{},[638,1183,644],{"stretchy":643},[646,1185,648],{},[592,1187,594],{},[638,1189,653],{"stretchy":643},[638,1191,656],{},[592,1193,636],{},[638,1195,640],{},[592,1197,594],{},[592,1199,744],{},[638,1201,640],{},[592,1203,594],{},[638,1205,955],{},[592,1207,744],{},[638,1209,640],{},[592,1211,594],{},[592,1213,636],{},[638,1215,640],{},[592,1217,594],{},[638,1219,656],{},[646,1221,648],{},[592,1223,636],{},[638,1225,640],{},[592,1227,594],{},[592,1229,744],{},[638,1231,640],{},[592,1233,594],{},[596,1235,1236],{"encoding":598},"\\sin(2x) = \\sin x \\cos x + \\cos x \\sin x = 2 \\sin x \\cos x",[573,1238,1240,1270,1307,1343],{"className":1239,"ariaHidden":603},[602],[573,1241,1243,1246,1249,1252,1255,1258,1261,1264,1267],{"className":1242},[607],[573,1244],{"className":1245,"style":675},[611],[573,1247,636],{"className":1248},[679],[573,1250,644],{"className":1251},[683],[573,1253,648],{"className":1254},[616],[573,1256,594],{"className":1257},[616,617],[573,1259,653],{"className":1260},[693],[573,1262],{"className":1263,"style":698},[697],[573,1265,656],{"className":1266},[702],[573,1268],{"className":1269,"style":698},[697],[573,1271,1273,1277,1280,1283,1286,1289,1292,1295,1298,1301,1304],{"className":1272},[607],[573,1274],{"className":1275,"style":1276},[611],"height:0.7512em;vertical-align:-0.0833em;",[573,1278,636],{"className":1279},[679],[573,1281],{"className":1282,"style":719},[697],[573,1284,594],{"className":1285},[616,617],[573,1287],{"className":1288,"style":719},[697],[573,1290,744],{"className":1291},[679],[573,1293],{"className":1294,"style":719},[697],[573,1296,594],{"className":1297},[616,617],[573,1299],{"className":1300,"style":1013},[697],[573,1302,955],{"className":1303},[1017],[573,1305],{"className":1306,"style":1013},[697],[573,1308,1310,1313,1316,1319,1322,1325,1328,1331,1334,1337,1340],{"className":1309},[607],[573,1311],{"className":1312,"style":712},[611],[573,1314,744],{"className":1315},[679],[573,1317],{"className":1318,"style":719},[697],[573,1320,594],{"className":1321},[616,617],[573,1323],{"className":1324,"style":719},[697],[573,1326,636],{"className":1327},[679],[573,1329],{"className":1330,"style":719},[697],[573,1332,594],{"className":1333},[616,617],[573,1335],{"className":1336,"style":698},[697],[573,1338,656],{"className":1339},[702],[573,1341],{"className":1342,"style":698},[697],[573,1344,1346,1349,1352,1355,1358,1361,1364,1367,1370,1373],{"className":1345},[607],[573,1347],{"className":1348,"style":712},[611],[573,1350,648],{"className":1351},[616],[573,1353],{"className":1354,"style":719},[697],[573,1356,636],{"className":1357},[679],[573,1359],{"className":1360,"style":719},[697],[573,1362,594],{"className":1363},[616,617],[573,1365],{"className":1366,"style":719},[697],[573,1368,744],{"className":1369},[679],[573,1371],{"className":1372,"style":719},[697],[573,1374,594],{"className":1375},[616,617],[559,1377,1379],{"id":1378},"beispiele","Beispiele",[564,1381,1382,1383,1411,1412,1488,1489,1160],{},"Für einen spitzen Winkel ",[573,1384,1386,1399],{"className":1385},[576],[573,1387,1389],{"className":1388},[580],[582,1390,1391],{"xmlns":584},[586,1392,1393,1397],{},[589,1394,1395],{},[592,1396,594],{},[596,1398,594],{"encoding":598},[573,1400,1402],{"className":1401,"ariaHidden":603},[602],[573,1403,1405,1408],{"className":1404},[607],[573,1406],{"className":1407,"style":612},[611],[573,1409,594],{"className":1410},[616,617]," gilt ",[573,1413,1415,1438],{"className":1414},[576],[573,1416,1418],{"className":1417},[580],[582,1419,1420],{"xmlns":584},[586,1421,1422,1435],{},[589,1423,1424,1426,1428,1430,1432],{},[592,1425,636],{},[638,1427,640],{},[592,1429,594],{},[638,1431,656],{},[646,1433,1434],{},"0,6",[596,1436,1437],{"encoding":598},"\\sin x = 0{,}6",[573,1439,1441,1465],{"className":1440,"ariaHidden":603},[602],[573,1442,1444,1447,1450,1453,1456,1459,1462],{"className":1443},[607],[573,1445],{"className":1446,"style":712},[611],[573,1448,636],{"className":1449},[679],[573,1451],{"className":1452,"style":719},[697],[573,1454,594],{"className":1455},[616,617],[573,1457],{"className":1458,"style":698},[697],[573,1460,656],{"className":1461},[702],[573,1463],{"className":1464,"style":698},[697],[573,1466,1468,1472,1476,1484],{"className":1467},[607],[573,1469],{"className":1470,"style":1471},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,1473,1475],{"className":1474},[616],"0",[573,1477,1479],{"className":1478},[616],[573,1480,1483],{"className":1481},[1482],"mpunct",",",[573,1485,1487],{"className":1486},[616],"6"," und damit ",[573,1490,1492,1515],{"className":1491},[576],[573,1493,1495],{"className":1494},[580],[582,1496,1497],{"xmlns":584},[586,1498,1499,1512],{},[589,1500,1501,1503,1505,1507,1509],{},[592,1502,744],{},[638,1504,640],{},[592,1506,594],{},[638,1508,656],{},[646,1510,1511],{},"0,8",[596,1513,1514],{"encoding":598},"\\cos x = 0{,}8",[573,1516,1518,1542],{"className":1517,"ariaHidden":603},[602],[573,1519,1521,1524,1527,1530,1533,1536,1539],{"className":1520},[607],[573,1522],{"className":1523,"style":612},[611],[573,1525,744],{"className":1526},[679],[573,1528],{"className":1529,"style":719},[697],[573,1531,594],{"className":1532},[616,617],[573,1534],{"className":1535,"style":698},[697],[573,1537,656],{"className":1538},[702],[573,1540],{"className":1541,"style":698},[697],[573,1543,1545,1548,1551,1557],{"className":1544},[607],[573,1546],{"className":1547,"style":1471},[611],[573,1549,1475],{"className":1550},[616],[573,1552,1554],{"className":1553},[616],[573,1555,1483],{"className":1556},[1482],[573,1558,1560],{"className":1559},[616],"8",[573,1562,1564],{"className":1563},[1164],[573,1565,1567,1609],{"className":1566},[576],[573,1568,1570],{"className":1569},[580],[582,1571,1572],{"xmlns":584,"display":1173},[586,1573,1574,1606],{},[589,1575,1576,1578,1580,1582,1584,1586,1588,1590,1592,1595,1597,1599,1601,1603],{},[592,1577,636],{},[638,1579,640],{},[638,1581,644],{"stretchy":643},[646,1583,648],{},[592,1585,594],{},[638,1587,653],{"stretchy":643},[638,1589,656],{},[646,1591,648],{},[638,1593,1594],{},"⋅",[646,1596,1434],{},[638,1598,1594],{},[646,1600,1511],{},[638,1602,656],{},[646,1604,1605],{},"0,96",[596,1607,1608],{"encoding":598},"\\sin(2x) = 2 \\cdot 0{,}6 \\cdot 0{,}8 = 0{,}96",[573,1610,1612,1642,1661,1688,1715],{"className":1611,"ariaHidden":603},[602],[573,1613,1615,1618,1621,1624,1627,1630,1633,1636,1639],{"className":1614},[607],[573,1616],{"className":1617,"style":675},[611],[573,1619,636],{"className":1620},[679],[573,1622,644],{"className":1623},[683],[573,1625,648],{"className":1626},[616],[573,1628,594],{"className":1629},[616,617],[573,1631,653],{"className":1632},[693],[573,1634],{"className":1635,"style":698},[697],[573,1637,656],{"className":1638},[702],[573,1640],{"className":1641,"style":698},[697],[573,1643,1645,1649,1652,1655,1658],{"className":1644},[607],[573,1646],{"className":1647,"style":1648},[611],"height:0.6444em;",[573,1650,648],{"className":1651},[616],[573,1653],{"className":1654,"style":1013},[697],[573,1656,1594],{"className":1657},[1017],[573,1659],{"className":1660,"style":1013},[697],[573,1662,1664,1667,1670,1676,1679,1682,1685],{"className":1663},[607],[573,1665],{"className":1666,"style":1471},[611],[573,1668,1475],{"className":1669},[616],[573,1671,1673],{"className":1672},[616],[573,1674,1483],{"className":1675},[1482],[573,1677,1487],{"className":1678},[616],[573,1680],{"className":1681,"style":1013},[697],[573,1683,1594],{"className":1684},[1017],[573,1686],{"className":1687,"style":1013},[697],[573,1689,1691,1694,1697,1703,1706,1709,1712],{"className":1690},[607],[573,1692],{"className":1693,"style":1471},[611],[573,1695,1475],{"className":1696},[616],[573,1698,1700],{"className":1699},[616],[573,1701,1483],{"className":1702},[1482],[573,1704,1560],{"className":1705},[616],[573,1707],{"className":1708,"style":698},[697],[573,1710,656],{"className":1711},[702],[573,1713],{"className":1714,"style":698},[697],[573,1716,1718,1721,1724,1730],{"className":1717},[607],[573,1719],{"className":1720,"style":1471},[611],[573,1722,1475],{"className":1723},[616],[573,1725,1727],{"className":1726},[616],[573,1728,1483],{"className":1729},[1482],[573,1731,1733],{"className":1732},[616],"96",[564,1735,1736,1737,1160],{},"Mit ",[573,1738,1740,1765],{"className":1739},[576],[573,1741,1743],{"className":1742},[580],[582,1744,1745],{"xmlns":584},[586,1746,1747,1762],{},[589,1748,1749,1751,1753],{},[592,1750,594],{},[638,1752,656],{},[1754,1755,1756,1759],"msup",{},[646,1757,1758],{},"30",[638,1760,1761],{},"∘",[596,1763,1764],{"encoding":598},"x = 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aber ",[573,2787,2789,2817],{"className":2788},[576],[573,2790,2792],{"className":2791},[580],[582,2793,2794],{"xmlns":584},[586,2795,2796,2814],{},[589,2797,2798,2800,2802,2808,2811],{},[592,2799,636],{},[638,2801,640],{},[1754,2803,2804,2806],{},[646,2805,1852],{},[638,2807,1761],{},[638,2809,2810],{},"≈",[646,2812,2813],{},"0,866",[596,2815,2816],{"encoding":598},"\\sin 60^\\circ \\approx 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Faktor ",[573,2896,2898,2911],{"className":2897},[576],[573,2899,2901],{"className":2900},[580],[582,2902,2903],{"xmlns":584},[586,2904,2905,2909],{},[589,2906,2907],{},[646,2908,648],{},[596,2910,648],{"encoding":598},[573,2912,2914],{"className":2913,"ariaHidden":603},[602],[573,2915,2917,2920],{"className":2916},[607],[573,2918],{"className":2919,"style":1648},[611],[573,2921,648],{"className":2922},[616]," vergessen: ",[573,2925,2927,2965],{"className":2926},[576],[573,2928,2930],{"className":2929},[580],[582,2931,2932],{"xmlns":584},[586,2933,2934,2962],{},[589,2935,2936,2938,2940,2942,2944,2946,2948,2950,2952,2954,2956,2958,2960],{},[592,2937,636],{},[638,2939,640],{},[638,2941,644],{"stretchy":643},[646,2943,648],{},[592,2945,594],{},[638,2947,653],{"stretchy":643},[638,2949,2491],{"mathvariant":2490},[592,2951,636],{},[638,2953,640],{},[592,2955,594],{},[592,2957,744],{},[638,2959,640],{},[592,2961,594],{},[596,2963,2964],{"encoding":598},"\\sin(2x) \\neq \\sin x \\cos x",[573,2966,2968,3031],{"className":2967,"ariaHidden":603},[602],[573,2969,2971,2974,2977,2980,2983,2986,2989,2992,3028],{"className":2970},[607],[573,2972],{"className":2973,"style":675},[611],[573,2975,636],{"className":2976},[679],[573,2978,644],{"className":2979},[683],[573,2981,648],{"className":2982},[616],[573,2984,594],{"className":2985},[616,617],[573,2987,653],{"className":2988},[693],[573,2990],{"className":2991,"style":698},[697],[573,2993,2995,3022,3025],{"className":2994},[702],[573,2996,2998],{"className":2997},[702],[573,2999,3001],{"className":3000},[616,2539],[573,3002,3004],{"className":3003},[2543],[573,3005,3007,3010,3019],{"className":3006},[2547],[573,3008],{"className":3009,"style":2551},[611],[573,3011,3013],{"className":3012},[2555],[573,3014,3016],{"className":3015},[616],[573,3017,2562],{"className":3018},[702],[573,3020],{"className":3021},[2566],[573,3023],{"className":3024},[697,2570],[573,3026,656],{"className":3027},[702],[573,3029],{"className":3030,"style":698},[697],[573,3032,3034,3037,3040,3043,3046,3049,3052,3055],{"className":3033},[607],[573,3035],{"className":3036,"style":712},[611],[573,3038,636],{"className":3039},[679],[573,3041],{"className":3042,"style":719},[697],[573,3044,594],{"className":3045},[616,617],[573,3047],{"className":3048,"style":719},[697],[573,3050,744],{"className":3051},[679],[573,3053],{"className":3054,"style":719},[697],[573,3056,594],{"className":3057},[616,617],[2433,3059,3060,3061,3100,3101,3140,3141,618],{},"Beim Lösen von Gleichungen durch ",[573,3062,3064,3082],{"className":3063},[576],[573,3065,3067],{"className":3066},[580],[582,3068,3069],{"xmlns":584},[586,3070,3071,3079],{},[589,3072,3073,3075,3077],{},[592,3074,636],{},[638,3076,640],{},[592,3078,594],{},[596,3080,3081],{"encoding":598},"\\sin x",[573,3083,3085],{"className":3084,"ariaHidden":603},[602],[573,3086,3088,3091,3094,3097],{"className":3087},[607],[573,3089],{"className":3090,"style":712},[611],[573,3092,636],{"className":3093},[679],[573,3095],{"className":3096,"style":719},[697],[573,3098,594],{"className":3099},[616,617]," oder ",[573,3102,3104,3122],{"className":3103},[576],[573,3105,3107],{"className":3106},[580],[582,3108,3109],{"xmlns":584},[586,3110,3111,3119],{},[589,3112,3113,3115,3117],{},[592,3114,744],{},[638,3116,640],{},[592,3118,594],{},[596,3120,3121],{"encoding":598},"\\cos x",[573,3123,3125],{"className":3124,"ariaHidden":603},[602],[573,3126,3128,3131,3134,3137],{"className":3127},[607],[573,3129],{"className":3130,"style":612},[611],[573,3132,744],{"className":3133},[679],[573,3135],{"className":3136,"style":719},[697],[573,3138,594],{"className":3139},[616,617]," teilen und so Lösungen verlieren. Besser ausklammern, z.B. ",[573,3142,3144,3211],{"className":3143},[576],[573,3145,3147],{"className":3146},[580],[582,3148,3149],{"xmlns":584},[586,3150,3151,3208],{},[589,3152,3153,3155,3157,3159,3161,3163,3165,3167,3170,3172,3174,3176,3178,3180,3182,3184,3188,3190,3192,3194,3196,3198,3200,3202,3204,3206],{},[646,3154,648],{},[592,3156,636],{},[638,3158,640],{},[592,3160,594],{},[592,3162,744],{},[638,3164,640],{},[592,3166,594],{},[638,3168,3169],{},"−",[592,3171,636],{},[638,3173,640],{},[592,3175,594],{},[638,3177,656],{},[592,3179,636],{},[638,3181,640],{},[592,3183,594],{},[3185,3186,3187],"mtext",{}," ",[638,3189,644],{"stretchy":643},[646,3191,648],{},[592,3193,744],{},[638,3195,640],{},[592,3197,594],{},[638,3199,3169],{},[646,3201,756],{},[638,3203,653],{"stretchy":643},[638,3205,656],{},[646,3207,1475],{},[596,3209,3210],{"encoding":598},"2 \\sin x \\cos x - \\sin x = \\sin x \\,(2 \\cos x - 1) = 0",[573,3212,3214,3256,3280,3325,3346],{"className":3213,"ariaHidden":603},[602],[573,3215,3217,3220,3223,3226,3229,3232,3235,3238,3241,3244,3247,3250,3253],{"className":3216},[607],[573,3218],{"className":3219,"style":1276},[611],[573,3221,648],{"className":3222},[616],[573,3224],{"className":3225,"style":719},[697],[573,3227,636],{"className":3228},[679],[573,3230],{"className":3231,"style":719},[697],[573,3233,594],{"className":3234},[616,617],[573,3236],{"className":3237,"style":719},[697],[573,3239,744],{"className":3240},[679],[573,3242],{"className":3243,"style":719},[697],[573,3245,594],{"className":3246},[616,617],[573,3248],{"className":3249,"style":1013},[697],[573,3251,3169],{"className":3252},[1017],[573,3254],{"className":3255,"style":1013},[697],[573,3257,3259,3262,3265,3268,3271,3274,3277],{"className":3258},[607],[573,3260],{"className":3261,"style":712},[611],[573,3263,636],{"className":3264},[679],[573,3266],{"className":3267,"style":719},[697],[573,3269,594],{"className":3270},[616,617],[573,3272],{"className":3273,"style":698},[697],[573,3275,656],{"className":3276},[702],[573,3278],{"className":3279,"style":698},[697],[573,3281,3283,3286,3289,3292,3295,3298,3301,3304,3307,3310,3313,3316,3319,3322],{"className":3282},[607],[573,3284],{"className":3285,"style":675},[611],[573,3287,636],{"className":3288},[679],[573,3290],{"className":3291,"style":719},[697],[573,3293,594],{"className":3294},[616,617],[573,3296],{"className":3297,"style":719},[697],[573,3299,644],{"className":3300},[683],[573,3302,648],{"className":3303},[616],[573,3305],{"className":3306,"style":719},[697],[573,3308,744],{"className":3309},[679],[573,3311],{"className":3312,"style":719},[697],[573,3314,594],{"className":3315},[616,617],[573,3317],{"className":3318,"style":1013},[697],[573,3320,3169],{"className":3321},[1017],[573,3323],{"className":3324,"style":1013},[697],[573,3326,3328,3331,3334,3337,3340,3343],{"className":3327},[607],[573,3329],{"className":3330,"style":675},[611],[573,3332,756],{"className":3333},[616],[573,3335,653],{"className":3336},[693],[573,3338],{"className":3339,"style":698},[697],[573,3341,656],{"className":3342},[702],[573,3344],{"className":3345,"style":698},[697],[573,3347,3349,3352],{"className":3348},[607],[573,3350],{"className":3351,"style":1648},[611],[573,3353,1475],{"className":3354},[616],{"title":3356,"searchDepth":3357,"depth":3357,"links":3358},"",2,[3359,3360,3361,3362],{"id":561,"depth":3357,"text":562},{"id":928,"depth":3357,"text":929},{"id":1378,"depth":3357,"text":1379},{"id":2427,"depth":3357,"text":2428},[3364,3367,3369,3372,3374,3377,3379,3381],{"lhs":3365,"rhs":3366},"sin(2*x)","2*sin(x)*cos(x)",{"lhs":3368,"rhs":3366},"sin(x)*cos(x) 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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>","TqF2tN2LQ65MB56EFsb-AmzkxZ4zQwZi9W9POW5n4rg",[3414,3417,3420,3423],{"stem":3415,"title":3416,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fadditionstheorem-kosinus","Additionstheorem für den Kosinus",{"stem":3418,"title":3419,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fadditionstheorem-sinus","Additionstheorem für den Sinus",{"stem":3421,"title":3422,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fdoppelwinkelformel-kosinus","Doppelwinkelformel für den 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