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oder ",[574,1169,1171,1190],{"className":1170},[577],[574,1172,1174],{"className":1173},[581],[583,1175,1176],{"xmlns":585},[587,1177,1178,1187],{},[590,1179,1180],{},[1100,1181,1182,1185],{},[1103,1183,1184],{},"75",[665,1186,1108],{},[597,1188,1189],{"encoding":599},"75^\\circ",[574,1191,1193],{"className":1192,"ariaHidden":604},[603],[574,1194,1196,1199,1203],{"className":1195},[608],[574,1197],{"className":1198,"style":1121},[612],[574,1200,1202],{"className":1201},[617],"7",[574,1204,1206,1209],{"className":1205},[617],[574,1207,1132],{"className":1208},[617],[574,1210,1212],{"className":1211},[1136],[574,1213,1215],{"className":1214},[1140],[574,1216,1218],{"className":1217},[1144],[574,1219,1221],{"className":1220,"style":1121},[1148],[574,1222,1223,1226],{"style":1151},[574,1224],{"className":1225,"style":1156},[1155],[574,1227,1229],{"className":1228},[1160,1161,1162,1163],[574,1230,1108],{"className":1231},[813,1163]," aus bekannten Werten bei ",[574,1234,1236,1255],{"className":1235},[577],[574,1237,1239],{"className":1238},[581],[583,1240,1241],{"xmlns":585},[587,1242,1243,1252],{},[590,1244,1245],{},[1100,1246,1247,1250],{},[1103,1248,1249],{},"30",[665,1251,1108],{},[597,1253,1254],{"encoding":599},"30^\\circ",[574,1256,1258],{"className":1257,"ariaHidden":604},[603],[574,1259,1261,1264,1268],{"className":1260},[608],[574,1262],{"className":1263,"style":1121},[612],[574,1265,1267],{"className":1266},[617],"3",[574,1269,1271,1275],{"className":1270},[617],[574,1272,1274],{"className":1273},[617],"0",[574,1276,1278],{"className":1277},[1136],[574,1279,1281],{"className":1280},[1140],[574,1282,1284],{"className":1283},[1144],[574,1285,1287],{"className":1286,"style":1121},[1148],[574,1288,1289,1292],{"style":1151},[574,1290],{"className":1291,"style":1156},[1155],[574,1293,1295],{"className":1294},[1160,1161,1162,1163],[574,1296,1108],{"className":1297},[813,1163],", ",[574,1300,1302,1321],{"className":1301},[577],[574,1303,1305],{"className":1304},[581],[583,1306,1307],{"xmlns":585},[587,1308,1309,1318],{},[590,1310,1311],{},[1100,1312,1313,1316],{},[1103,1314,1315],{},"45",[665,1317,1108],{},[597,1319,1320],{"encoding":599},"45^\\circ",[574,1322,1324],{"className":1323,"ariaHidden":604},[603],[574,1325,1327,1330,1334],{"className":1326},[608],[574,1328],{"className":1329,"style":1121},[612],[574,1331,1333],{"className":1332},[617],"4",[574,1335,1337,1340],{"className":1336},[617],[574,1338,1132],{"className":1339},[617],[574,1341,1343],{"className":1342},[1136],[574,1344,1346],{"className":1345},[1140],[574,1347,1349],{"className":1348},[1144],[574,1350,1352],{"className":1351,"style":1121},[1148],[574,1353,1354,1357],{"style":1151},[574,1355],{"className":1356,"style":1156},[1155],[574,1358,1360],{"className":1359},[1160,1161,1162,1163],[574,1361,1108],{"className":1362},[813,1163],[574,1364,1366,1385],{"className":1365},[577],[574,1367,1369],{"className":1368},[581],[583,1370,1371],{"xmlns":585},[587,1372,1373,1382],{},[590,1374,1375],{},[1100,1376,1377,1380],{},[1103,1378,1379],{},"60",[665,1381,1108],{},[597,1383,1384],{"encoding":599},"60^\\circ",[574,1386,1388],{"className":1387,"ariaHidden":604},[603],[574,1389,1391,1394,1398],{"className":1390},[608],[574,1392],{"className":1393,"style":1121},[612],[574,1395,1397],{"className":1396},[617],"6",[574,1399,1401,1404],{"className":1400},[617],[574,1402,1274],{"className":1403},[617],[574,1405,1407],{"className":1406},[1136],[574,1408,1410],{"className":1409},[1140],[574,1411,1413],{"className":1412},[1144],[574,1414,1416],{"className":1415,"style":1121},[1148],[574,1417,1418,1421],{"style":1151},[574,1419],{"className":1420,"style":1156},[1155],[574,1422,1424],{"className":1423},[1160,1161,1162,1163],[574,1425,1108],{"className":1426},[813,1163],[1084,1428,1429,1430,750],{},"Herleitung der Doppelwinkelformeln (mit ",[574,1431,1433,1451],{"className":1432},[577],[574,1434,1436],{"className":1435},[581],[583,1437,1438],{"xmlns":585},[587,1439,1440,1448],{},[590,1441,1442,1444,1446],{},[593,1443,634],{},[665,1445,753],{},[593,1447,595],{},[597,1449,1450],{"encoding":599},"y = x",[574,1452,1454,1472],{"className":1453,"ariaHidden":604},[603],[574,1455,1457,1460,1463,1466,1469],{"className":1456},[608],[574,1458],{"className":1459,"style":646},[612],[574,1461,634],{"className":1462,"style":650},[617,618],[574,1464],{"className":1465,"style":833},[808],[574,1467,753],{"className":1468},[837],[574,1470],{"className":1471,"style":833},[808],[574,1473,1475,1478],{"className":1474},[608],[574,1476],{"className":1477,"style":613},[612],[574,1479,595],{"className":1480},[617,618],[1084,1482,1483],{},"Umformen trigonometrischer Terme, z.B. beim Ableiten oder Integrieren",[560,1485,1487],{"id":1486},"herleitung","Herleitung",[565,1489,1490,1491,1526,1527,1555,1556,1584,1585,619,1668,714],{},"Die Formel für die Differenz folgt aus der Formel für die Summe, wenn man ",[574,1492,1494,1510],{"className":1493},[577],[574,1495,1497],{"className":1496},[581],[583,1498,1499],{"xmlns":585},[587,1500,1501,1507],{},[590,1502,1503,1505],{},[665,1504,698],{},[593,1506,634],{},[597,1508,1509],{"encoding":599},"-y",[574,1511,1513],{"className":1512,"ariaHidden":604},[603],[574,1514,1516,1520,1523],{"className":1515},[608],[574,1517],{"className":1518,"style":1519},[612],"height:0.7778em;vertical-align:-0.1944em;",[574,1521,698],{"className":1522},[617],[574,1524,634],{"className":1525,"style":650},[617,618]," statt ",[574,1528,1530,1543],{"className":1529},[577],[574,1531,1533],{"className":1532},[581],[583,1534,1535],{"xmlns":585},[587,1536,1537,1541],{},[590,1538,1539],{},[593,1540,634],{},[597,1542,634],{"encoding":599},[574,1544,1546],{"className":1545,"ariaHidden":604},[603],[574,1547,1549,1552],{"className":1548},[608],[574,1550],{"className":1551,"style":646},[612],[574,1553,634],{"className":1554,"style":650},[617,618]," einsetzt. Dabei nutzt man, dass der Kosinus achsensymmetrisch (zur ",[574,1557,1559,1572],{"className":1558},[577],[574,1560,1562],{"className":1561},[581],[583,1563,1564],{"xmlns":585},[587,1565,1566,1570],{},[590,1567,1568],{},[593,1569,634],{},[597,1571,634],{"encoding":599},[574,1573,1575],{"className":1574,"ariaHidden":604},[603],[574,1576,1578,1581],{"className":1577},[608],[574,1579],{"className":1580,"style":646},[612],[574,1582,634],{"className":1583,"style":650},[617,618],"-Achse) und der Sinus punktsymmetrisch (zum Ursprung) ist: ",[574,1586,1588,1620],{"className":1587},[577],[574,1589,1591],{"className":1590},[581],[583,1592,1593],{"xmlns":585},[587,1594,1595,1617],{},[590,1596,1597,1599,1601,1603,1605,1607,1609,1611,1613,1615],{},[593,1598,762],{},[665,1600,737],{},[665,1602,741],{"stretchy":740},[665,1604,698],{},[593,1606,634],{},[665,1608,750],{"stretchy":740},[665,1610,753],{},[593,1612,762],{},[665,1614,737],{},[593,1616,634],{},[597,1618,1619],{"encoding":599},"\\cos(-y) = \\cos y",[574,1621,1623,1653],{"className":1622,"ariaHidden":604},[603],[574,1624,1626,1629,1632,1635,1638,1641,1644,1647,1650],{"className":1625},[608],[574,1627],{"className":1628,"style":793},[612],[574,1630,762],{"className":1631},[797],[574,1633,741],{"className":1634},[801],[574,1636,698],{"className":1637},[617],[574,1639,634],{"className":1640,"style":650},[617,618],[574,1642,750],{"className":1643},[829],[574,1645],{"className":1646,"style":833},[808],[574,1648,753],{"className":1649},[837],[574,1651],{"className":1652,"style":833},[808],[574,1654,1656,1659,1662,1665],{"className":1655},[608],[574,1657],{"className":1658,"style":646},[612],[574,1660,762],{"className":1661},[797],[574,1663],{"className":1664,"style":854},[808],[574,1666,634],{"className":1667,"style":650},[617,618],[574,1669,1671,1705],{"className":1670},[577],[574,1672,1674],{"className":1673},[581],[583,1675,1676],{"xmlns":585},[587,1677,1678,1702],{},[590,1679,1680,1682,1684,1686,1688,1690,1692,1694,1696,1698,1700],{},[593,1681,734],{},[665,1683,737],{},[665,1685,741],{"stretchy":740},[665,1687,698],{},[593,1689,634],{},[665,1691,750],{"stretchy":740},[665,1693,753],{},[665,1695,698],{},[593,1697,734],{},[665,1699,737],{},[593,1701,634],{},[597,1703,1704],{"encoding":599},"\\sin(-y) = -\\sin y",[574,1706,1708,1738],{"className":1707,"ariaHidden":604},[603],[574,1709,1711,1714,1717,1720,1723,1726,1729,1732,1735],{"className":1710},[608],[574,1712],{"className":1713,"style":793},[612],[574,1715,734],{"className":1716},[797],[574,1718,741],{"className":1719},[801],[574,1721,698],{"className":1722},[617],[574,1724,634],{"className":1725,"style":650},[617,618],[574,1727,750],{"className":1728},[829],[574,1730],{"className":1731,"style":833},[808],[574,1733,753],{"className":1734},[837],[574,1736],{"className":1737,"style":833},[808],[574,1739,1741,1744,1747,1750,1753,1756],{"className":1740},[608],[574,1742],{"className":1743,"style":847},[612],[574,1745,698],{"className":1746},[617],[574,1748],{"className":1749,"style":854},[808],[574,1751,734],{"className":1752},[797],[574,1754],{"className":1755,"style":854},[808],[574,1757,634],{"className":1758,"style":650},[617,618],[560,1760,1762],{"id":1761},"beispiele","Beispiele",[565,1764,1765,1766,1838,1839,2012],{},"Exakter Wert von ",[574,1767,1769,1791],{"className":1768},[577],[574,1770,1772],{"className":1771},[581],[583,1773,1774],{"xmlns":585},[587,1775,1776,1788],{},[590,1777,1778,1780,1782],{},[593,1779,734],{},[665,1781,737],{},[1100,1783,1784,1786],{},[1103,1785,1184],{},[665,1787,1108],{},[597,1789,1790],{"encoding":599},"\\sin 75^\\circ",[574,1792,1794],{"className":1793,"ariaHidden":604},[603],[574,1795,1797,1800,1803,1806,1809],{"className":1796},[608],[574,1798],{"className":1799,"style":1121},[612],[574,1801,734],{"className":1802},[797],[574,1804],{"className":1805,"style":854},[808],[574,1807,1202],{"className":1808},[617],[574,1810,1812,1815],{"className":1811},[617],[574,1813,1132],{"className":1814},[617],[574,1816,1818],{"className":1817},[1136],[574,1819,1821],{"className":1820},[1140],[574,1822,1824],{"className":1823},[1144],[574,1825,1827],{"className":1826,"style":1121},[1148],[574,1828,1829,1832],{"style":1151},[574,1830],{"className":1831,"style":1156},[1155],[574,1833,1835],{"className":1834},[1160,1161,1162,1163],[574,1836,1108],{"className":1837},[813,1163]," mit ",[574,1840,1842,1876],{"className":1841},[577],[574,1843,1845],{"className":1844},[581],[583,1846,1847],{"xmlns":585},[587,1848,1849,1873],{},[590,1850,1851,1857,1859,1865,1867],{},[1100,1852,1853,1855],{},[1103,1854,1184],{},[665,1856,1108],{},[665,1858,753],{},[1100,1860,1861,1863],{},[1103,1862,1315],{},[665,1864,1108],{},[665,1866,667],{},[1100,1868,1869,1871],{},[1103,1870,1249],{},[665,1872,1108],{},[597,1874,1875],{"encoding":599},"75^\\circ = 45^\\circ + 30^\\circ",[574,1877,1879,1926,1974],{"className":1878,"ariaHidden":604},[603],[574,1880,1882,1885,1888,1917,1920,1923],{"className":1881},[608],[574,1883],{"className":1884,"style":1121},[612],[574,1886,1202],{"className":1887},[617],[574,1889,1891,1894],{"className":1890},[617],[574,1892,1132],{"className":1893},[617],[574,1895,1897],{"className":1896},[1136],[574,1898,1900],{"className":1899},[1140],[574,1901,1903],{"className":1902},[1144],[574,1904,1906],{"className":1905,"style":1121},[1148],[574,1907,1908,1911],{"style":1151},[574,1909],{"className":1910,"style":1156},[1155],[574,1912,1914],{"className":1913},[1160,1161,1162,1163],[574,1915,1108],{"className":1916},[813,1163],[574,1918],{"className":1919,"style":833},[808],[574,1921,753],{"className":1922},[837],[574,1924],{"className":1925,"style":833},[808],[574,1927,1929,1933,1936,1965,1968,1971],{"className":1928},[608],[574,1930],{"className":1931,"style":1932},[612],"height:0.7574em;vertical-align:-0.0833em;",[574,1934,1333],{"className":1935},[617],[574,1937,1939,1942],{"className":1938},[617],[574,1940,1132],{"className":1941},[617],[574,1943,1945],{"className":1944},[1136],[574,1946,1948],{"className":1947},[1140],[574,1949,1951],{"className":1950},[1144],[574,1952,1954],{"className":1953,"style":1121},[1148],[574,1955,1956,1959],{"style":1151},[574,1957],{"className":1958,"style":1156},[1155],[574,1960,1962],{"className":1961},[1160,1161,1162,1163],[574,1963,1108],{"className":1964},[813,1163],[574,1966],{"className":1967,"style":809},[808],[574,1969,667],{"className":1970},[813],[574,1972],{"className":1973,"style":809},[808],[574,1975,1977,1980,1983],{"className":1976},[608],[574,1978],{"className":1979,"style":1121},[612],[574,1981,1267],{"className":1982},[617],[574,1984,1986,1989],{"className":1985},[617],[574,1987,1274],{"className":1988},[617],[574,1990,1992],{"className":1991},[1136],[574,1993,1995],{"className":1994},[1140],[574,1996,1998],{"className":1997},[1144],[574,1999,2001],{"className":2000,"style":1121},[1148],[574,2002,2003,2006],{"style":1151},[574,2004],{"className":2005,"style":1156},[1155],[574,2007,2009],{"className":2008},[1160,1161,1162,1163],[574,2010,1108],{"className":2011},[813,1163],":",[574,2014,2016],{"className":2015},[718],[574,2017,2019,2145],{"className":2018},[577],[574,2020,2022],{"className":2021},[581],[583,2023,2024],{"xmlns":585,"display":727},[587,2025,2026,2142],{},[590,2027,2028,2030,2032,2038,2040,2042,2044,2050,2052,2054,2060,2062,2064,2066,2072,2074,2076,2082,2084,2095,2098,2106,2108,2116,2118,2124,2126],{},[593,2029,734],{},[665,2031,737],{},[1100,2033,2034,2036],{},[1103,2035,1184],{},[665,2037,1108],{},[665,2039,753],{},[593,2041,734],{},[665,2043,737],{},[1100,2045,2046,2048],{},[1103,2047,1315],{},[665,2049,1108],{},[593,2051,762],{},[665,2053,737],{},[1100,2055,2056,2058],{},[1103,2057,1249],{},[665,2059,1108],{},[665,2061,667],{},[593,2063,762],{},[665,2065,737],{},[1100,2067,2068,2070],{},[1103,2069,1315],{},[665,2071,1108],{},[593,2073,734],{},[665,2075,737],{},[1100,2077,2078,2080],{},[1103,2079,1249],{},[665,2081,1108],{},[665,2083,753],{},[2085,2086,2087,2093],"mfrac",{},[2088,2089,2090],"msqrt",{},[1103,2091,2092],{},"2",[1103,2094,2092],{},[665,2096,2097],{},"⋅",[2085,2099,2100,2104],{},[2088,2101,2102],{},[1103,2103,1267],{},[1103,2105,2092],{},[665,2107,667],{},[2085,2109,2110,2114],{},[2088,2111,2112],{},[1103,2113,2092],{},[1103,2115,2092],{},[665,2117,2097],{},[2085,2119,2120,2122],{},[1103,2121,1125],{},[1103,2123,2092],{},[665,2125,753],{},[2085,2127,2128,2140],{},[590,2129,2130,2134,2136],{},[2088,2131,2132],{},[1103,2133,1397],{},[665,2135,667],{},[2088,2137,2138],{},[1103,2139,2092],{},[1103,2141,1333],{},[597,2143,2144],{"encoding":599},"\\sin 75^\\circ = \\sin 45^\\circ \\cos 30^\\circ + \\cos 45^\\circ \\sin 30^\\circ\n= \\frac{\\sqrt{2}}{2} \\cdot \\frac{\\sqrt{3}}{2} + \\frac{\\sqrt{2}}{2} \\cdot \\frac{1}{2}\n= \\frac{\\sqrt{6} + 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