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y) - \\cos(x + y)\\right]",[578,1279,1281,1317],{"className":1280,"ariaHidden":608},[607],[578,1282,1284,1287,1290,1293,1296,1299,1302,1305,1308,1311,1314],{"className":1283},[612],[578,1285],{"className":1286,"style":757},[616],[578,1288,675],{"className":1289},[761],[578,1291],{"className":1292,"style":766},[765],[578,1294,599],{"className":1295},[621,622],[578,1297],{"className":1298,"style":766},[765],[578,1300,675],{"className":1301},[761],[578,1303],{"className":1304,"style":766},[765],[578,1306,638],{"className":1307,"style":654},[621,622],[578,1309],{"className":1310,"style":785},[765],[578,1312,691],{"className":1313},[789],[578,1315],{"className":1316,"style":785},[765],[578,1318,1320,1323,1385,1388],{"className":1319},[612],[578,1321],{"className":1322,"style":799},[616],[578,1324,1326,1329,1382],{"className":1325},[621],[578,1327],{"className":1328},[806,807],[578,1330,1332],{"className":1331},[693],[578,1333,1335,1374],{"className":1334},[814,815],[578,1336,1338,1371],{"className":1337},[819],[578,1339,1341,1352,1360],{"className":1340,"style":824},[823],[578,1342,1343,1346],{"style":827},[578,1344],{"className":1345,"style":832},[831],[578,1347,1349],{"className":1348},[621],[578,1350,701],{"className":1351},[621],[578,1353,1354,1357],{"style":841},[578,1355],{"className":1356,"style":832},[831],[578,1358],{"className":1359,"style":849},[848],[578,1361,1362,1365],{"style":852},[578,1363],{"className":1364,"style":832},[831],[578,1366,1368],{"className":1367},[621],[578,1369,698],{"className":1370},[621],[578,1372,866],{"className":1373},[865],[578,1375,1377],{"className":1376},[819],[578,1378,1380],{"className":1379,"style":873},[823],[578,1381],{},[578,1383],{"className":1384},[879,807],[578,1386],{"className":1387,"style":766},[765],[578,1389,1391,1394,1397,1400,1403,1406,1409,1412,1415,1418,1421,1424,1427,1430,1433,1436,1439,1442,1445,1448,1451],{"className":1390},[886],[578,1392,706],{"className":1393,"style":891},[806,890],[578,1395,684],{"className":1396},[761],[578,1398,714],{"className":1399},[806],[578,1401,599],{"className":1402},[621,622],[578,1404],{"className":1405,"style":904},[765],[578,1407,719],{"className":1408},[908],[578,1410],{"className":1411,"style":904},[765],[578,1413,638],{"className":1414,"style":654},[621,622],[578,1416,724],{"className":1417},[879],[578,1419],{"className":1420,"style":904},[765],[578,1422,719],{"className":1423},[908],[578,1425],{"className":1426,"style":904},[765],[578,1428,684],{"className":1429},[761],[578,1431,714],{"className":1432},[806],[578,1434,599],{"className":1435},[621,622],[578,1437],{"className":1438,"style":904},[765],[578,1440,727],{"className":1441},[908],[578,1443],{"className":1444,"style":904},[765],[578,1446,638],{"className":1447,"style":654},[621,622],[578,1449,724],{"className":1450},[879],[578,1452,744],{"className":1453,"style":891},[879,890],[565,1455,1456,1457,1460,1461,1532],{},"Der wichtigste Einsatz ist die ",[569,1458,1459],{},"Integration",": Ein Produkt wie ",[578,1462,1464,1495],{"className":1463},[581],[578,1465,1467],{"className":1466},[585],[587,1468,1469],{"xmlns":589},[591,1470,1471,1492],{},[594,1472,1473,1475,1477,1479,1482,1484,1486,1488,1490],{},[597,1474,675],{},[677,1476,679],{},[677,1478,714],{"stretchy":713},[696,1480,1481],{},"3",[597,1483,599],{},[677,1485,724],{"stretchy":713},[597,1487,684],{},[677,1489,679],{},[597,1491,599],{},[601,1493,1494],{"encoding":603},"\\sin(3x)\\cos x",[578,1496,1498],{"className":1497,"ariaHidden":608},[607],[578,1499,1501,1505,1508,1511,1514,1517,1520,1523,1526,1529],{"className":1500},[612],[578,1502],{"className":1503,"style":1504},[616],"height:1em;vertical-align:-0.25em;",[578,1506,675],{"className":1507},[761],[578,1509,714],{"className":1510},[806],[578,1512,1481],{"className":1513},[621],[578,1515,599],{"className":1516},[621,622],[578,1518,724],{"className":1519},[879],[578,1521],{"className":1522,"style":766},[765],[578,1524,684],{"className":1525},[761],[578,1527],{"className":1528,"style":766},[765],[578,1530,599],{"className":1531},[621,622]," hat keine direkte Stammfunktion, eine Summe von Sinustermen schon. Auch bei Fourierreihen und in der Signalverarbeitung (Mischen zweier Frequenzen) braucht man diese Formeln.",[565,1534,1535,1536,1587,1588,1825],{},"Mit ",[578,1537,1539,1557],{"className":1538},[581],[578,1540,1542],{"className":1541},[585],[587,1543,1544],{"xmlns":589},[591,1545,1546,1554],{},[594,1547,1548,1550,1552],{},[597,1549,638],{},[677,1551,691],{},[597,1553,599],{},[601,1555,1556],{"encoding":603},"y = x",[578,1558,1560,1578],{"className":1559,"ariaHidden":608},[607],[578,1561,1563,1566,1569,1572,1575],{"className":1562},[612],[578,1564],{"className":1565,"style":650},[616],[578,1567,638],{"className":1568,"style":654},[621,622],[578,1570],{"className":1571,"style":785},[765],[578,1573,691],{"className":1574},[789],[578,1576],{"className":1577,"style":785},[765],[578,1579,1581,1584],{"className":1580},[612],[578,1582],{"className":1583,"style":617},[616],[578,1585,599],{"className":1586},[621,622]," ergeben sich die Formeln zur Potenzreduktion, z.B. ",[578,1589,1591,1646],{"className":1590},[581],[578,1592,1594],{"className":1593},[585],[587,1595,1596],{"xmlns":589},[591,1597,1598,1643],{},[594,1599,1600,1611,1613,1615,1621],{},[1601,1602,1603,1609],"msup",{},[594,1604,1605,1607],{},[597,1606,675],{},[677,1608,679],{},[696,1610,701],{},[597,1612,599],{},[677,1614,691],{},[693,1616,1617,1619],{},[696,1618,698],{},[696,1620,701],{},[594,1622,1623,1625,1627,1629,1631,1633,1635,1637,1639,1641],{},[677,1624,706],{"fence":608},[696,1626,698],{},[677,1628,719],{},[597,1630,684],{},[677,1632,679],{},[677,1634,714],{"stretchy":713},[696,1636,701],{},[597,1638,599],{},[677,1640,724],{"stretchy":713},[677,1642,744],{"fence":608},[601,1644,1645],{"encoding":603},"\\sin^2 x = \\frac{1}{2}\\left[1 - \\cos(2x)\\right]",[578,1647,1649,1707],{"className":1648,"ariaHidden":608},[607],[578,1650,1652,1656,1692,1695,1698,1701,1704],{"className":1651},[612],[578,1653],{"className":1654,"style":1655},[616],"height:0.8719em;",[578,1657,1659,1662],{"className":1658},[761],[578,1660,675],{"className":1661},[761],[578,1663,1666],{"className":1664},[1665],"msupsub",[578,1667,1669],{"className":1668},[814],[578,1670,1672],{"className":1671},[819],[578,1673,1675],{"className":1674,"style":1655},[823],[578,1676,1678,1682],{"style":1677},"top:-3.1208em;margin-right:0.05em;",[578,1679],{"className":1680,"style":1681},[831],"height:2.7em;",[578,1683,1689],{"className":1684},[1685,1686,1687,1688],"sizing","reset-size6","size3","mtight",[578,1690,701],{"className":1691},[621,1688],[578,1693],{"className":1694,"style":766},[765],[578,1696,599],{"className":1697},[621,622],[578,1699],{"className":1700,"style":785},[765],[578,1702,691],{"className":1703},[789],[578,1705],{"className":1706,"style":785},[765],[578,1708,1710,1714,1786,1789],{"className":1709},[612],[578,1711],{"className":1712,"style":1713},[616],"height:1.1901em;vertical-align:-0.345em;",[578,1715,1717,1720,1783],{"className":1716},[621],[578,1718],{"className":1719},[806,807],[578,1721,1723],{"className":1722},[693],[578,1724,1726,1774],{"className":1725},[814,815],[578,1727,1729,1771],{"className":1728},[819],[578,1730,1733,1748,1756],{"className":1731,"style":1732},[823],"height:0.8451em;",[578,1734,1736,1739],{"style":1735},"top:-2.655em;",[578,1737],{"className":1738,"style":832},[831],[578,1740,1742],{"className":1741},[1685,1686,1687,1688],[578,1743,1745],{"className":1744},[621,1688],[578,1746,701],{"className":1747},[621,1688],[578,1749,1750,1753],{"style":841},[578,1751],{"className":1752,"style":832},[831],[578,1754],{"className":1755,"style":849},[848],[578,1757,1759,1762],{"style":1758},"top:-3.394em;",[578,1760],{"className":1761,"style":832},[831],[578,1763,1765],{"className":1764},[1685,1686,1687,1688],[578,1766,1768],{"className":1767},[621,1688],[578,1769,698],{"className":1770},[621,1688],[578,1772,866],{"className":1773},[865],[578,1775,1777],{"className":1776},[819],[578,1778,1781],{"className":1779,"style":1780},[823],"height:0.345em;",[578,1782],{},[578,1784],{"className":1785},[879,807],[578,1787],{"className":1788,"style":766},[765],[578,1790,1792,1795,1798,1801,1804,1807,1810,1813,1816,1819,1822],{"className":1791},[886],[578,1793,706],{"className":1794,"style":891},[806,890],[578,1796,698],{"className":1797},[621],[578,1799],{"className":1800,"style":904},[765],[578,1802,719],{"className":1803},[908],[578,1805],{"className":1806,"style":904},[765],[578,1808,684],{"className":1809},[761],[578,1811,714],{"className":1812},[806],[578,1814,701],{"className":1815},[621],[578,1817,599],{"className":1818},[621,622],[578,1820,724],{"className":1821},[879],[578,1823,744],{"className":1824,"style":891},[879,890],".",[560,1827,1829],{"id":1828},"herleitung","Herleitung",[565,1831,1832],{},"Man addiert oder subtrahiert zwei Additionstheoreme, sodass sich ein Teil weghebt. Zum Beispiel:",[578,1834,1836],{"className":1835},[659],[578,1837,1839,1961],{"className":1838},[581],[578,1840,1842],{"className":1841},[585],[587,1843,1844],{"xmlns":589,"display":668},[591,1845,1846,1958],{},[594,1847,1848,1850,1852,1854,1856,1858,1860,1862,1864,1866,1868,1870,1872,1874,1876,1878,1880,1882,1884,1886,1888,1890,1892,1894,1896,1898,1900,1902,1904,1906,1908,1910,1912,1914,1916,1918,1920,1922,1924,1926,1928,1930,1932,1934,1936,1938,1940,1942,1944,1946,1948,1950,1952,1954,1956],{},[597,1849,684],{},[677,1851,679],{},[677,1853,714],{"stretchy":713},[597,1855,599],{},[677,1857,719],{},[597,1859,638],{},[677,1861,724],{"stretchy":713},[677,1863,719],{},[597,1865,684],{},[677,1867,679],{},[677,1869,714],{"stretchy":713},[597,1871,599],{},[677,1873,727],{},[597,1875,638],{},[677,1877,724],{"stretchy":713},[677,1879,691],{},[677,1881,714],{"stretchy":713},[597,1883,684],{},[677,1885,679],{},[597,1887,599],{},[597,1889,684],{},[677,1891,679],{},[597,1893,638],{},[677,1895,727],{},[597,1897,675],{},[677,1899,679],{},[597,1901,599],{},[597,1903,675],{},[677,1905,679],{},[597,1907,638],{},[677,1909,724],{"stretchy":713},[677,1911,719],{},[677,1913,714],{"stretchy":713},[597,1915,684],{},[677,1917,679],{},[597,1919,599],{},[597,1921,684],{},[677,1923,679],{},[597,1925,638],{},[677,1927,719],{},[597,1929,675],{},[677,1931,679],{},[597,1933,599],{},[597,1935,675],{},[677,1937,679],{},[597,1939,638],{},[677,1941,724],{"stretchy":713},[677,1943,691],{},[696,1945,701],{},[597,1947,675],{},[677,1949,679],{},[597,1951,599],{},[597,1953,675],{},[677,1955,679],{},[597,1957,638],{},[601,1959,1960],{"encoding":603},"\\cos(x - y) - \\cos(x + y) = (\\cos x \\cos y + \\sin x \\sin y) - (\\cos x \\cos y - \\sin x \\sin y) = 2 \\sin x \\sin y",[578,1962,1964,1988,2009,2033,2054,2093,2132,2171,2210],{"className":1963,"ariaHidden":608},[607],[578,1965,1967,1970,1973,1976,1979,1982,1985],{"className":1966},[612],[578,1968],{"className":1969,"style":1504},[616],[578,1971,684],{"className":1972},[761],[578,1974,714],{"className":1975},[806],[578,1977,599],{"className":1978},[621,622],[578,1980],{"className":1981,"style":904},[765],[578,1983,719],{"className":1984},[908],[578,1986],{"className":1987,"style":904},[765],[578,1989,1991,1994,1997,2000,2003,2006],{"className":1990},[612],[578,1992],{"className":1993,"style":1504},[616],[578,1995,638],{"className":1996,"style":654},[621,622],[578,1998,724],{"className":1999},[879],[578,2001],{"className":2002,"style":904},[765],[578,2004,719],{"className":2005},[908],[578,2007],{"className":2008,"style":904},[765],[578,2010,2012,2015,2018,2021,2024,2027,2030],{"className":2011},[612],[578,2013],{"className":2014,"style":1504},[616],[578,2016,684],{"className":2017},[761],[578,2019,714],{"className":2020},[806],[578,2022,599],{"className":2023},[621,622],[578,2025],{"className":2026,"style":904},[765],[578,2028,727],{"className":2029},[908],[578,2031],{"className":2032,"style":904},[765],[578,2034,2036,2039,2042,2045,2048,2051],{"className":2035},[612],[578,2037],{"className":2038,"style":1504},[616],[578,2040,638],{"className":2041,"style":654},[621,622],[578,2043,724],{"className":2044},[879],[578,2046],{"className":2047,"style":785},[765],[578,2049,691],{"className":2050},[789],[578,2052],{"className":2053,"style":785},[765],[578,2055,2057,2060,2063,2066,2069,2072,2075,2078,2081,2084,2087,2090],{"className":2056},[612],[578,2058],{"className":2059,"style":1504},[616],[578,2061,714],{"className":2062},[806],[578,2064,684],{"className":2065},[761],[578,2067],{"className":2068,"style":766},[765],[578,2070,599],{"className":2071},[621,622],[578,2073],{"className":2074,"style":766},[765],[578,2076,684],{"className":2077},[761],[578,2079],{"className":2080,"style":766},[765],[578,2082,638],{"className":2083,"style":654},[621,622],[578,2085],{"className":2086,"style":904},[765],[578,2088,727],{"className":2089},[908],[578,2091],{"className":2092,"style":904},[765],[578,2094,2096,2099,2102,2105,2108,2111,2114,2117,2120,2123,2126,2129],{"className":2095},[612],[578,2097],{"className":2098,"style":1504},[616],[578,2100,675],{"className":2101},[761],[578,2103],{"className":2104,"style":766},[765],[578,2106,599],{"className":2107},[621,622],[578,2109],{"className":2110,"style":766},[765],[578,2112,675],{"className":2113},[761],[578,2115],{"className":2116,"style":766},[765],[578,2118,638],{"className":2119,"style":654},[621,622],[578,2121,724],{"className":2122},[879],[578,2124],{"className":2125,"style":904},[765],[578,2127,719],{"className":2128},[908],[578,2130],{"className":2131,"style":904},[765],[578,2133,2135,2138,2141,2144,2147,2150,2153,2156,2159,2162,2165,2168],{"className":2134},[612],[578,2136],{"className":2137,"style":1504},[616],[578,2139,714],{"className":2140},[806],[578,2142,684],{"className":2143},[761],[578,2145],{"className":2146,"style":766},[765],[578,2148,599],{"className":2149},[621,622],[578,2151],{"className":2152,"style":766},[765],[578,2154,684],{"className":2155},[761],[578,2157],{"className":2158,"style":766},[765],[578,2160,638],{"className":2161,"style":654},[621,622],[578,2163],{"className":2164,"style":904},[765],[578,2166,719],{"className":2167},[908],[578,2169],{"className":2170,"style":904},[765],[578,2172,2174,2177,2180,2183,2186,2189,2192,2195,2198,2201,2204,2207],{"className":2173},[612],[578,2175],{"className":2176,"style":1504},[616],[578,2178,675],{"className":2179},[761],[578,2181],{"className":2182,"style":766},[765],[578,2184,599],{"className":2185},[621,622],[578,2187],{"className":2188,"style":766},[765],[578,2190,675],{"className":2191},[761],[578,2193],{"className":2194,"style":766},[765],[578,2196,638],{"className":2197,"style":654},[621,622],[578,2199,724],{"className":2200},[879],[578,2202],{"className":2203,"style":785},[765],[578,2205,691],{"className":2206},[789],[578,2208],{"className":2209,"style":785},[765],[578,2211,2213,2216,2219,2222,2225,2228,2231,2234,2237,2240],{"className":2212},[612],[578,2214],{"className":2215,"style":757},[616],[578,2217,701],{"className":2218},[621],[578,2220],{"className":2221,"style":766},[765],[578,2223,675],{"className":2224},[761],[578,2226],{"className":2227,"style":766},[765],[578,2229,599],{"className":2230},[621,622],[578,2232],{"className":2233,"style":766},[765],[578,2235,675],{"className":2236},[761],[578,2238],{"className":2239,"style":766},[765],[578,2241,638],{"className":2242,"style":654},[621,622],[565,2244,2245,2246,2275,2276,623,2405,1825],{},"Teilen durch ",[578,2247,2249,2262],{"className":2248},[581],[578,2250,2252],{"className":2251},[585],[587,2253,2254],{"xmlns":589},[591,2255,2256,2260],{},[594,2257,2258],{},[696,2259,701],{},[601,2261,701],{"encoding":603},[578,2263,2265],{"className":2264,"ariaHidden":608},[607],[578,2266,2268,2272],{"className":2267},[612],[578,2269],{"className":2270,"style":2271},[616],"height:0.6444em;",[578,2273,701],{"className":2274},[621]," ergibt die dritte Formel. Die beiden anderen folgen genauso aus ",[578,2277,2279,2321],{"className":2278},[581],[578,2280,2282],{"className":2281},[585],[587,2283,2284],{"xmlns":589},[591,2285,2286,2318],{},[594,2287,2288,2290,2292,2294,2296,2298,2300,2302,2304,2306,2308,2310,2312,2314,2316],{},[597,2289,684],{},[677,2291,679],{},[677,2293,714],{"stretchy":713},[597,2295,599],{},[677,2297,719],{},[597,2299,638],{},[677,2301,724],{"stretchy":713},[677,2303,727],{},[597,2305,684],{},[677,2307,679],{},[677,2309,714],{"stretchy":713},[597,2311,599],{},[677,2313,727],{},[597,2315,638],{},[677,2317,724],{"stretchy":713},[601,2319,2320],{"encoding":603},"\\cos(x - y) + \\cos(x + y)",[578,2322,2324,2348,2369,2393],{"className":2323,"ariaHidden":608},[607],[578,2325,2327,2330,2333,2336,2339,2342,2345],{"className":2326},[612],[578,2328],{"className":2329,"style":1504},[616],[578,2331,684],{"className":2332},[761],[578,2334,714],{"className":2335},[806],[578,2337,599],{"className":2338},[621,622],[578,2340],{"className":2341,"style":904},[765],[578,2343,719],{"className":2344},[908],[578,2346],{"className":2347,"style":904},[765],[578,2349,2351,2354,2357,2360,2363,2366],{"className":2350},[612],[578,2352],{"className":2353,"style":1504},[616],[578,2355,638],{"className":2356,"style":654},[621,622],[578,2358,724],{"className":2359},[879],[578,2361],{"className":2362,"style":904},[765],[578,2364,727],{"className":2365},[908],[578,2367],{"className":2368,"style":904},[765],[578,2370,2372,2375,2378,2381,2384,2387,2390],{"className":2371},[612],[578,2373],{"className":2374,"style":1504},[616],[578,2376,684],{"className":2377},[761],[578,2379,714],{"className":2380},[806],[578,2382,599],{"className":2383},[621,622],[578,2385],{"className":2386,"style":904},[765],[578,2388,727],{"className":2389},[908],[578,2391],{"className":2392,"style":904},[765],[578,2394,2396,2399,2402],{"className":2395},[612],[578,2397],{"className":2398,"style":1504},[616],[578,2400,638],{"className":2401,"style":654},[621,622],[578,2403,724],{"className":2404},[879],[578,2406,2408,2450],{"className":2407},[581],[578,2409,2411],{"className":2410},[585],[587,2412,2413],{"xmlns":589},[591,2414,2415,2447],{},[594,2416,2417,2419,2421,2423,2425,2427,2429,2431,2433,2435,2437,2439,2441,2443,2445],{},[597,2418,675],{},[677,2420,679],{},[677,2422,714],{"stretchy":713},[597,2424,599],{},[677,2426,719],{},[597,2428,638],{},[677,2430,724],{"stretchy":713},[677,2432,727],{},[597,2434,675],{},[677,2436,679],{},[677,2438,714],{"stretchy":713},[597,2440,599],{},[677,2442,727],{},[597,2444,638],{},[677,2446,724],{"stretchy":713},[601,2448,2449],{"encoding":603},"\\sin(x - y) + \\sin(x + y)",[578,2451,2453,2477,2498,2522],{"className":2452,"ariaHidden":608},[607],[578,2454,2456,2459,2462,2465,2468,2471,2474],{"className":2455},[612],[578,2457],{"className":2458,"style":1504},[616],[578,2460,675],{"className":2461},[761],[578,2463,714],{"className":2464},[806],[578,2466,599],{"className":2467},[621,622],[578,2469],{"className":2470,"style":904},[765],[578,2472,719],{"className":2473},[908],[578,2475],{"className":2476,"style":904},[765],[578,2478,2480,2483,2486,2489,2492,2495],{"className":2479},[612],[578,2481],{"className":2482,"style":1504},[616],[578,2484,638],{"className":2485,"style":654},[621,622],[578,2487,724],{"className":2488},[879],[578,2490],{"className":2491,"style":904},[765],[578,2493,727],{"className":2494},[908],[578,2496],{"className":2497,"style":904},[765],[578,2499,2501,2504,2507,2510,2513,2516,2519],{"className":2500},[612],[578,2502],{"className":2503,"style":1504},[616],[578,2505,675],{"className":2506},[761],[578,2508,714],{"className":2509},[806],[578,2511,599],{"className":2512},[621,622],[578,2514],{"className":2515,"style":904},[765],[578,2517,727],{"className":2518},[908],[578,2520],{"className":2521,"style":904},[765],[578,2523,2525,2528,2531],{"className":2524},[612],[578,2526],{"className":2527,"style":1504},[616],[578,2529,638],{"className":2530,"style":654},[621,622],[578,2532,724],{"className":2533},[879],[560,2535,2537],{"id":2536},"beispiele","Beispiele",[578,2539,2541],{"className":2540},[659],[578,2542,2544,2651],{"className":2543},[581],[578,2545,2547],{"className":2546},[585],[587,2548,2549],{"xmlns":589,"display":668},[591,2550,2551,2648],{},[594,2552,2553,2555,2557,2565,2567,2569,2576,2578,2584,2614,2616,2622,2639,2641],{},[597,2554,684],{},[677,2556,679],{},[1601,2558,2559,2562],{},[696,2560,2561],{},"75",[677,2563,2564],{},"∘",[597,2566,684],{},[677,2568,679],{},[1601,2570,2571,2574],{},[696,2572,2573],{},"15",[677,2575,2564],{},[677,2577,691],{},[693,2579,2580,2582],{},[696,2581,698],{},[696,2583,701],{},[594,2585,2586,2588,2590,2592,2599,2601,2603,2605,2612],{},[677,2587,706],{"fence":608},[597,2589,684],{},[677,2591,679],{},[1601,2593,2594,2597],{},[696,2595,2596],{},"60",[677,2598,2564],{},[677,2600,727],{},[597,2602,684],{},[677,2604,679],{},[1601,2606,2607,2610],{},[696,2608,2609],{},"90",[677,2611,2564],{},[677,2613,744],{"fence":608},[677,2615,691],{},[693,2617,2618,2620],{},[696,2619,698],{},[696,2621,701],{},[594,2623,2624,2626,2632,2634,2637],{},[677,2625,706],{"fence":608},[693,2627,2628,2630],{},[696,2629,698],{},[696,2631,701],{},[677,2633,727],{},[696,2635,2636],{},"0",[677,2638,744],{"fence":608},[677,2640,691],{},[693,2642,2643,2645],{},[696,2644,698],{},[696,2646,2647],{},"4",[601,2649,2650],{"encoding":603},"\\cos 75^\\circ \\cos 15^\\circ = \\frac{1}{2}\\left[\\cos 60^\\circ + \\cos 90^\\circ\\right] = \\frac{1}{2}\\left[\\frac{1}{2} + 0\\right] = \\frac{1}{4}",[578,2652,2654,2752,2928,3099],{"className":2653,"ariaHidden":608},[607],[578,2655,2657,2661,2664,2667,2671,2702,2705,2708,2711,2714,2743,2746,2749],{"className":2656},[612],[578,2658],{"className":2659,"style":2660},[616],"height:0.7241em;",[578,2662,684],{"className":2663},[761],[578,2665],{"className":2666,"style":766},[765],[578,2668,2670],{"className":2669},[621],"7",[578,2672,2674,2678],{"className":2673},[621],[578,2675,2677],{"className":2676},[621],"5",[578,2679,2681],{"className":2680},[1665],[578,2682,2684],{"className":2683},[814],[578,2685,2687],{"className":2686},[819],[578,2688,2690],{"className":2689,"style":2660},[823],[578,2691,2693,2696],{"style":2692},"top:-3.113em;margin-right:0.05em;",[578,2694],{"className":2695,"style":1681},[831],[578,2697,2699],{"className":2698},[1685,1686,1687,1688],[578,2700,2564],{"className":2701},[908,1688],[578,2703],{"className":2704,"style":766},[765],[578,2706,684],{"className":2707},[761],[578,2709],{"className":2710,"style":766},[765],[578,2712,698],{"className":2713},[621],[578,2715,2717,2720],{"className":2716},[621],[578,2718,2677],{"className":2719},[621],[578,2721,2723],{"className":2722},[1665],[578,2724,2726],{"className":2725},[814],[578,2727,2729],{"className":2728},[819],[578,2730,2732],{"className":2731,"style":2660},[823],[578,2733,2734,2737],{"style":2692},[578,2735],{"className":2736,"style":1681},[831],[578,2738,2740],{"className":2739},[1685,1686,1687,1688],[578,2741,2564],{"className":2742},[908,1688],[578,2744],{"className":2745,"style":785},[765],[578,2747,691],{"className":2748},[789],[578,2750],{"className":2751,"style":785},[765],[578,2753,2755,2758,2820,2823,2919,2922,2925],{"className":2754},[612],[578,2756],{"className":2757,"style":799},[616],[578,2759,2761,2764,2817],{"className":2760},[621],[578,2762],{"className":2763},[806,807],[578,2765,2767],{"className":2766},[693],[578,2768,2770,2809],{"className":2769},[814,815],[578,2771,2773,2806],{"className":2772},[819],[578,2774,2776,2787,2795],{"className":2775,"style":824},[823],[578,2777,2778,2781],{"style":827},[578,2779],{"className":2780,"style":832},[831],[578,2782,2784],{"className":2783},[621],[578,2785,701],{"className":2786},[621],[578,2788,2789,2792],{"style":841},[578,2790],{"className":2791,"style":832},[831],[578,2793],{"className":2794,"style":849},[848],[578,2796,2797,2800],{"style":852},[578,2798],{"className":2799,"style":832},[831],[578,2801,2803],{"className":2802},[621],[578,2804,698],{"className":2805},[621],[578,2807,866],{"className":2808},[865],[578,2810,2812],{"className":2811},[819],[578,2813,2815],{"className":2814,"style":873},[823],[578,2816],{},[578,2818],{"className":2819},[879,807],[578,2821],{"className":2822,"style":766},[765],[578,2824,2826,2829,2832,2835,2839,2868,2871,2874,2877,2880,2883,2887,2916],{"className":2825},[886],[578,2827,706],{"className":2828,"style":891},[806,890],[578,2830,684],{"className":2831},[761],[578,2833],{"className":2834,"style":766},[765],[578,2836,2838],{"className":2837},[621],"6",[578,2840,2842,2845],{"className":2841},[621],[578,2843,2636],{"className":2844},[621],[578,2846,2848],{"className":2847},[1665],[578,2849,2851],{"className":2850},[814],[578,2852,2854],{"className":2853},[819],[578,2855,2857],{"className":2856,"style":2660},[823],[578,2858,2859,2862],{"style":2692},[578,2860],{"className":2861,"style":1681},[831],[578,2863,2865],{"className":2864},[1685,1686,1687,1688],[578,2866,2564],{"className":2867},[908,1688],[578,2869],{"className":2870,"style":904},[765],[578,2872,727],{"className":2873},[908],[578,2875],{"className":2876,"style":904},[765],[578,2878,684],{"className":2879},[761],[578,2881],{"className":2882,"style":766},[765],[578,2884,2886],{"className":2885},[621],"9",[578,2888,2890,2893],{"className":2889},[621],[578,2891,2636],{"className":2892},[621],[578,2894,2896],{"className":2895},[1665],[578,2897,2899],{"className":2898},[814],[578,2900,2902],{"className":2901},[819],[578,2903,2905],{"className":2904,"style":2660},[823],[578,2906,2907,2910],{"style":2692},[578,2908],{"className":2909,"style":1681},[831],[578,2911,2913],{"className":2912},[1685,1686,1687,1688],[578,2914,2564],{"className":2915},[908,1688],[578,2917,744],{"className":2918,"style":891},[879,890],[578,2920],{"className":2921,"style":785},[765],[578,2923,691],{"className":2924},[789],[578,2926],{"className":2927,"style":785},[765],[578,2929,2931,2935,2997,3000,3090,3093,3096],{"className":2930},[612],[578,2932],{"className":2933,"style":2934},[616],"height:2.4em;vertical-align:-0.95em;",[578,2936,2938,2941,2994],{"className":2937},[621],[578,2939],{"className":2940},[806,807],[578,2942,2944],{"className":2943},[693],[578,2945,2947,2986],{"className":2946},[814,815],[578,2948,2950,2983],{"className":2949},[819],[578,2951,2953,2964,2972],{"className":2952,"style":824},[823],[578,2954,2955,2958],{"style":827},[578,2956],{"className":2957,"style":832},[831],[578,2959,2961],{"className":2960},[621],[578,2962,701],{"className":2963},[621],[578,2965,2966,2969],{"style":841},[578,2967],{"className":2968,"style":832},[831],[578,2970],{"className":2971,"style":849},[848],[578,2973,2974,2977],{"style":852},[578,2975],{"className":2976,"style":832},[831],[578,2978,2980],{"className":2979},[621],[578,2981,698],{"className":2982},[621],[578,2984,866],{"className":2985},[865],[578,2987,2989],{"className":2988},[819],[578,2990,2992],{"className":2991,"style":873},[823],[578,2993],{},[578,2995],{"className":2996},[879,807],[578,2998],{"className":2999,"style":766},[765],[578,3001,3003,3010,3072,3075,3078,3081,3084],{"className":3002},[886],[578,3004,3006],{"className":3005,"style":891},[806,890],[578,3007,706],{"className":3008},[3009,1687],"delimsizing",[578,3011,3013,3016,3069],{"className":3012},[621],[578,3014],{"className":3015},[806,807],[578,3017,3019],{"className":3018},[693],[578,3020,3022,3061],{"className":3021},[814,815],[578,3023,3025,3058],{"className":3024},[819],[578,3026,3028,3039,3047],{"className":3027,"style":824},[823],[578,3029,3030,3033],{"style":827},[578,3031],{"className":3032,"style":832},[831],[578,3034,3036],{"className":3035},[621],[578,3037,701],{"className":3038},[621],[578,3040,3041,3044],{"style":841},[578,3042],{"className":3043,"style":832},[831],[578,3045],{"className":3046,"style":849},[848],[578,3048,3049,3052],{"style":852},[578,3050],{"className":3051,"style":832},[831],[578,3053,3055],{"className":3054},[621],[578,3056,698],{"className":3057},[621],[578,3059,866],{"className":3060},[865],[578,3062,3064],{"className":3063},[819],[578,3065,3067],{"className":3066,"style":873},[823],[578,3068],{},[578,3070],{"className":3071},[879,807],[578,3073],{"className":3074,"style":904},[765],[578,3076,727],{"className":3077},[908],[578,3079],{"className":3080,"style":904},[765],[578,3082,2636],{"className":3083},[621],[578,3085,3087],{"className":3086,"style":891},[879,890],[578,3088,744],{"className":3089},[3009,1687],[578,3091],{"className":3092,"style":785},[765],[578,3094,691],{"className":3095},[789],[578,3097],{"className":3098,"style":785},[765],[578,3100,3102,3105],{"className":3101},[612],[578,3103],{"className":3104,"style":799},[616],[578,3106,3108,3111,3164],{"className":3107},[621],[578,3109],{"className":3110},[806,807],[578,3112,3114],{"className":3113},[693],[578,3115,3117,3156],{"className":3116},[814,815],[578,3118,3120,3153],{"className":3119},[819],[578,3121,3123,3134,3142],{"className":3122,"style":824},[823],[578,3124,3125,3128],{"style":827},[578,3126],{"className":3127,"style":832},[831],[578,3129,3131],{"className":3130},[621],[578,3132,2647],{"className":3133},[621],[578,3135,3136,3139],{"style":841},[578,3137],{"className":3138,"style":832},[831],[578,3140],{"className":3141,"style":849},[848],[578,3143,3144,3147],{"style":852},[578,3145],{"className":3146,"style":832},[831],[578,3148,3150],{"className":3149},[621],[578,3151,698],{"className":3152},[621],[578,3154,866],{"className":3155},[865],[578,3157,3159],{"className":3158},[819],[578,3160,3162],{"className":3161,"style":873},[823],[578,3163],{},[578,3165],{"className":3166},[879,807],[578,3168,3170],{"className":3169},[659],[578,3171,3173,3249],{"className":3172},[581],[578,3174,3176],{"className":3175},[585],[587,3177,3178],{"xmlns":589,"display":668},[591,3179,3180,3246],{},[594,3181,3182,3184,3186,3192,3194,3196,3202,3204,3210,3238,3240],{},[597,3183,675],{},[677,3185,679],{},[1601,3187,3188,3190],{},[696,3189,2561],{},[677,3191,2564],{},[597,3193,675],{},[677,3195,679],{},[1601,3197,3198,3200],{},[696,3199,2573],{},[677,3201,2564],{},[677,3203,691],{},[693,3205,3206,3208],{},[696,3207,698],{},[696,3209,701],{},[594,3211,3212,3214,3216,3218,3224,3226,3228,3230,3236],{},[677,3213,706],{"fence":608},[597,3215,684],{},[677,3217,679],{},[1601,3219,3220,3222],{},[696,3221,2596],{},[677,3223,2564],{},[677,3225,719],{},[597,3227,684],{},[677,3229,679],{},[1601,3231,3232,3234],{},[696,3233,2609],{},[677,3235,2564],{},[677,3237,744],{"fence":608},[677,3239,691],{},[693,3241,3242,3244],{},[696,3243,698],{},[696,3245,2647],{},[601,3247,3248],{"encoding":603},"\\sin 75^\\circ \\sin 15^\\circ = \\frac{1}{2}\\left[\\cos 60^\\circ - \\cos 90^\\circ\\right] = \\frac{1}{4}",[578,3250,3252,3346,3520],{"className":3251,"ariaHidden":608},[607],[578,3253,3255,3258,3261,3264,3267,3296,3299,3302,3305,3308,3337,3340,3343],{"className":3254},[612],[578,3256],{"className":3257,"style":2660},[616],[578,3259,675],{"className":3260},[761],[578,3262],{"className":3263,"style":766},[765],[578,3265,2670],{"className":3266},[621],[578,3268,3270,3273],{"className":3269},[621],[578,3271,2677],{"className":3272},[621],[578,3274,3276],{"className":3275},[1665],[578,3277,3279],{"className":3278},[814],[578,3280,3282],{"className":3281},[819],[578,3283,3285],{"className":3284,"style":2660},[823],[578,3286,3287,3290],{"style":2692},[578,3288],{"className":3289,"style":1681},[831],[578,3291,3293],{"className":3292},[1685,1686,1687,1688],[578,3294,2564],{"className":3295},[908,1688],[578,3297],{"className":3298,"style":766},[765],[578,3300,675],{"className":3301},[761],[578,3303],{"className":3304,"style":766},[765],[578,3306,698],{"className":3307},[621],[578,3309,3311,3314],{"className":3310},[621],[578,3312,2677],{"className":3313},[621],[578,3315,3317],{"className":3316},[1665],[578,3318,3320],{"className":3319},[814],[578,3321,3323],{"className":3322},[819],[578,3324,3326],{"className":3325,"style":2660},[823],[578,3327,3328,3331],{"style":2692},[578,3329],{"className":3330,"style":1681},[831],[578,3332,3334],{"className":3333},[1685,1686,1687,1688],[578,3335,2564],{"className":3336},[908,1688],[578,3338],{"className":3339,"style":785},[765],[578,3341,691],{"className":3342},[789],[578,3344],{"className":3345,"style":785},[765],[578,3347,3349,3352,3414,3417,3511,3514,3517],{"className":3348},[612],[578,3350],{"className":3351,"style":799},[616],[578,3353,3355,3358,3411],{"className":3354},[621],[578,3356],{"className":3357},[806,807],[578,3359,3361],{"className":3360},[693],[578,3362,3364,3403],{"className":3363},[814,815],[578,3365,3367,3400],{"className":3366},[819],[578,3368,3370,3381,3389],{"className":3369,"style":824},[823],[578,3371,3372,3375],{"style":827},[578,3373],{"className":3374,"style":832},[831],[578,3376,3378],{"className":3377},[621],[578,3379,701],{"className":3380},[621],[578,3382,3383,3386],{"style":841},[578,3384],{"className":3385,"style":832},[831],[578,3387],{"className":3388,"style":849},[848],[578,3390,3391,3394],{"style":852},[578,3392],{"className":3393,"style":832},[831],[578,3395,3397],{"className":3396},[621],[578,3398,698],{"className":3399},[621],[578,3401,866],{"className":3402},[865],[578,3404,3406],{"className":3405},[819],[578,3407,3409],{"className":3408,"style":873},[823],[578,3410],{},[578,3412],{"className":3413},[879,807],[578,3415],{"className":3416,"style":766},[765],[578,3418,3420,3423,3426,3429,3432,3461,3464,3467,3470,3473,3476,3479,3508],{"className":3419},[886],[578,3421,706],{"className":3422,"style":891},[806,890],[578,3424,684],{"className":3425},[761],[578,3427],{"className":3428,"style":766},[765],[578,3430,2838],{"className":3431},[621],[578,3433,3435,3438],{"className":3434},[621],[578,3436,2636],{"className":3437},[621],[578,3439,3441],{"className":3440},[1665],[578,3442,3444],{"className":3443},[814],[578,3445,3447],{"className":3446},[819],[578,3448,3450],{"className":3449,"style":2660},[823],[578,3451,3452,3455],{"style":2692},[578,3453],{"className":3454,"style":1681},[831],[578,3456,3458],{"className":3457},[1685,1686,1687,1688],[578,3459,2564],{"className":3460},[908,1688],[578,3462],{"className":3463,"style":904},[765],[578,3465,719],{"className":3466},[908],[578,3468],{"className":3469,"style":904},[765],[578,3471,684],{"className":3472},[761],[578,3474],{"className":3475,"style":766},[765],[578,3477,2886],{"className":3478},[621],[578,3480,3482,3485],{"className":3481},[621],[578,3483,2636],{"className":3484},[621],[578,3486,3488],{"className":3487},[1665],[578,3489,3491],{"className":3490},[814],[578,3492,3494],{"className":3493},[819],[578,3495,3497],{"className":3496,"style":2660},[823],[578,3498,3499,3502],{"style":2692},[578,3500],{"className":3501,"style":1681},[831],[578,3503,3505],{"className":3504},[1685,1686,1687,1688],[578,3506,2564],{"className":3507},[908,1688],[578,3509,744],{"className":3510,"style":891},[879,890],[578,3512],{"className":3513,"style":785},[765],[578,3515,691],{"className":3516},[789],[578,3518],{"className":3519,"style":785},[765],[578,3521,3523,3526],{"className":3522},[612],[578,3524],{"className":3525,"style":799},[616],[578,3527,3529,3532,3585],{"className":3528},[621],[578,3530],{"className":3531},[806,807],[578,3533,3535],{"className":3534},[693],[578,3536,3538,3577],{"className":3537},[814,815],[578,3539,3541,3574],{"className":3540},[819],[578,3542,3544,3555,3563],{"className":3543,"style":824},[823],[578,3545,3546,3549],{"style":827},[578,3547],{"className":3548,"style":832},[831],[578,3550,3552],{"className":3551},[621],[578,3553,2647],{"className":3554},[621],[578,3556,3557,3560],{"style":841},[578,3558],{"className":3559,"style":832},[831],[578,3561],{"className":3562,"style":849},[848],[578,3564,3565,3568],{"style":852},[578,3566],{"className":3567,"style":832},[831],[578,3569,3571],{"className":3570},[621],[578,3572,698],{"className":3573},[621],[578,3575,866],{"className":3576},[865],[578,3578,3580],{"className":3579},[819],[578,3581,3583],{"className":3582,"style":873},[823],[578,3584],{},[578,3586],{"className":3587},[879,807],[565,3589,3590],{},"Integral eines Produkts:",[578,3592,3594],{"className":3593},[659],[578,3595,3597,3806],{"className":3596},[581],[578,3598,3600],{"className":3599},[585],[587,3601,3602],{"xmlns":589,"display":668},[591,3603,3604,3803],{},[594,3605,3606,3625,3627,3629,3631,3633,3635,3637,3639,3641,3643,3647,3650,3652,3654,3660,3674,3706,3708,3710,3712,3771,3773,3779,3781,3795,3797],{},[3607,3608,3609,3612,3614],"msubsup",{},[677,3610,3611],{},"∫",[696,3613,2636],{},[594,3615,3616,3619,3623],{},[597,3617,3618],{},"π",[597,3620,3622],{"mathvariant":3621},"normal","\u002F",[696,3624,701],{},[597,3626,675],{},[677,3628,679],{},[677,3630,714],{"stretchy":713},[696,3632,1481],{},[597,3634,599],{},[677,3636,724],{"stretchy":713},[597,3638,684],{},[677,3640,679],{},[597,3642,599],{},[3644,3645,3646],"mtext",{}," ",[597,3648,3649],{"mathvariant":3621},"d",[597,3651,599],{},[677,3653,691],{},[693,3655,3656,3658],{},[696,3657,698],{},[696,3659,701],{},[3607,3661,3662,3664,3666],{},[677,3663,3611],{},[696,3665,2636],{},[594,3667,3668,3670,3672],{},[597,3669,3618],{},[597,3671,3622],{"mathvariant":3621},[696,3673,701],{},[594,3675,3676,3678,3680,3682,3684,3686,3688,3690,3692,3694,3696,3698,3700,3702,3704],{},[677,3677,706],{"fence":608},[597,3679,675],{},[677,3681,679],{},[677,3683,714],{"stretchy":713},[696,3685,701],{},[597,3687,599],{},[677,3689,724],{"stretchy":713},[677,3691,727],{},[597,3693,675],{},[677,3695,679],{},[677,3697,714],{"stretchy":713},[696,3699,2647],{},[597,3701,599],{},[677,3703,724],{"stretchy":713},[677,3705,744],{"fence":608},[597,3707,3649],{"mathvariant":3621},[597,3709,599],{},[677,3711,691],{},[3607,3713,3714,3761,3763],{},[594,3715,3716,3718,3720,3738,3740,3759],{},[677,3717,706],{"fence":608},[677,3719,719],{},[693,3721,3722,3736],{},[594,3723,3724,3726,3728,3730,3732,3734],{},[597,3725,684],{},[677,3727,679],{},[677,3729,714],{"stretchy":713},[696,3731,701],{},[597,3733,599],{},[677,3735,724],{"stretchy":713},[696,3737,2647],{},[677,3739,719],{},[693,3741,3742,3756],{},[594,3743,3744,3746,3748,3750,3752,3754],{},[597,3745,684],{},[677,3747,679],{},[677,3749,714],{"stretchy":713},[696,3751,2647],{},[597,3753,599],{},[677,3755,724],{"stretchy":713},[696,3757,3758],{},"8",[677,3760,744],{"fence":608},[696,3762,2636],{},[594,3764,3765,3767,3769],{},[597,3766,3618],{},[597,3768,3622],{"mathvariant":3621},[696,3770,701],{},[677,3772,691],{},[693,3774,3775,3777],{},[696,3776,698],{},[696,3778,3758],{},[677,3780,719],{},[594,3782,3783,3785,3787,3793],{},[677,3784,714],{"fence":608},[677,3786,719],{},[693,3788,3789,3791],{},[696,3790,1481],{},[696,3792,3758],{},[677,3794,724],{"fence":608},[677,3796,691],{},[693,3798,3799,3801],{},[696,3800,698],{},[696,3802,701],{},[601,3804,3805],{"encoding":603},"\\int_0^{\\pi\u002F2} \\sin(3x) \\cos x \\,\\mathrm{d}x\n= \\frac{1}{2} \\int_0^{\\pi\u002F2} \\left[\\sin(2x) + \\sin(4x)\\right] \\mathrm{d}x\n= \\left[-\\frac{\\cos(2x)}{4} - \\frac{\\cos(4x)}{8}\\right]_0^{\\pi\u002F2}\n= \\frac{1}{8} - \\left(-\\frac{3}{8}\\right) = 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nicht umgekehrt. Probe mit ",[578,4919,4921,4947],{"className":4920},[581],[578,4922,4924],{"className":4923},[585],[587,4925,4926],{"xmlns":589},[591,4927,4928,4944],{},[594,4929,4930,4932,4934,4936,4938],{},[597,4931,599],{},[677,4933,691],{},[597,4935,638],{},[677,4937,691],{},[693,4939,4940,4942],{},[597,4941,3618],{},[696,4943,701],{},[601,4945,4946],{"encoding":603},"x = y = \\frac{\\pi}{2}",[578,4948,4950,4968,4986],{"className":4949,"ariaHidden":608},[607],[578,4951,4953,4956,4959,4962,4965],{"className":4952},[612],[578,4954],{"className":4955,"style":617},[616],[578,4957,599],{"className":4958},[621,622],[578,4960],{"className":4961,"style":785},[765],[578,4963,691],{"className":4964},[789],[578,4966],{"className":4967,"style":785},[765],[578,4969,4971,4974,4977,4980,4983],{"className":4970},[612],[578,4972],{"className":4973,"style":650},[616],[578,4975,638],{"className":4976,"style":654},[621,622],[578,4978],{"className":4979,"style":785},[765],[578,4981,691],{"className":4982},[789],[578,4984],{"className":4985,"style":785},[765],[578,4987,4989,4993],{"className":4988},[612],[578,4990],{"className":4991,"style":4992},[616],"height:1.0404em;vertical-align:-0.345em;",[578,4994,4996,4999,5059],{"className":4995},[621],[578,4997],{"className":4998},[806,807],[578,5000,5002],{"className":5001},[693],[578,5003,5005,5051],{"className":5004},[814,815],[578,5006,5008,5048],{"className":5007},[819],[578,5009,5012,5026,5034],{"className":5010,"style":5011},[823],"height:0.6954em;",[578,5013,5014,5017],{"style":1735},[578,5015],{"className":5016,"style":832},[831],[578,5018,5020],{"className":5019},[1685,1686,1687,1688],[578,5021,5023],{"className":5022},[621,1688],[578,5024,701],{"className":5025},[621,1688],[578,5027,5028,5031],{"style":841},[578,5029],{"className":5030,"style":832},[831],[578,5032],{"className":5033,"style":849},[848],[578,5035,5036,5039],{"style":1758},[578,5037],{"className":5038,"style":832},[831],[578,5040,5042],{"className":5041},[1685,1686,1687,1688],[578,5043,5045],{"className":5044},[621,1688],[578,5046,3618],{"className":5047,"style":654},[621,622,1688],[578,5049,866],{"className":5050},[865],[578,5052,5054],{"className":5053},[819],[578,5055,5057],{"className":5056,"style":1780},[823],[578,5058],{},[578,5060],{"className":5061},[879,807],": links ",[578,5064,5066,5079],{"className":5065},[581],[578,5067,5069],{"className":5068},[585],[587,5070,5071],{"xmlns":589},[591,5072,5073,5077],{},[594,5074,5075],{},[696,5076,698],{},[601,5078,698],{"encoding":603},[578,5080,5082],{"className":5081,"ariaHidden":608},[607],[578,5083,5085,5088],{"className":5084},[612],[578,5086],{"className":5087,"style":2271},[616],[578,5089,698],{"className":5090},[621],", rechts ",[578,5093,5095,5133],{"className":5094},[581],[578,5096,5098],{"className":5097},[585],[587,5099,5100],{"xmlns":589},[591,5101,5102,5130],{},[594,5103,5104,5110,5112,5114,5116,5118,5120,5122,5124,5126,5128],{},[693,5105,5106,5108],{},[696,5107,698],{},[696,5109,701],{},[677,5111,706],{"stretchy":713},[696,5113,698],{},[677,5115,719],{},[677,5117,714],{"stretchy":713},[677,5119,719],{},[696,5121,698],{},[677,5123,724],{"stretchy":713},[677,5125,744],{"stretchy":713},[677,5127,691],{},[696,5129,698],{},[601,5131,5132],{"encoding":603},"\\frac{1}{2}[1 - 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Für ",[578,5410,5412,5438],{"className":5411},[581],[578,5413,5415],{"className":5414},[585],[587,5416,5417],{"xmlns":589},[591,5418,5419,5435],{},[594,5420,5421,5423,5425,5427,5429],{},[597,5422,599],{},[677,5424,691],{},[597,5426,638],{},[677,5428,691],{},[1601,5430,5431,5433],{},[696,5432,2596],{},[677,5434,2564],{},[601,5436,5437],{"encoding":603},"x = y = 60^\\circ",[578,5439,5441,5459,5477],{"className":5440,"ariaHidden":608},[607],[578,5442,5444,5447,5450,5453,5456],{"className":5443},[612],[578,5445],{"className":5446,"style":617},[616],[578,5448,599],{"className":5449},[621,622],[578,5451],{"className":5452,"style":785},[765],[578,5454,691],{"className":5455},[789],[578,5457],{"className":5458,"style":785},[765],[578,5460,5462,5465,5468,5471,5474],{"className":5461},[612],[578,5463],{"className":5464,"style":650},[616],[578,5466,638],{"className":5467,"style":654},[621,622],[578,5469],{"className":5470,"style":785},[765],[578,5472,691],{"className":5473},[789],[578,5475],{"className":5476,"style":785},[765],[578,5478,5480,5484,5487],{"className":5479},[612],[578,5481],{"className":5482,"style":5483},[616],"height:0.6741em;",[578,5485,2838],{"className":5486},[621],[578,5488,5490,5493],{"className":5489},[621],[578,5491,2636],{"className":5492},[621],[578,5494,5496],{"className":5495},[1665],[578,5497,5499],{"className":5498},[814],[578,5500,5502],{"className":5501},[819],[578,5503,5505],{"className":5504,"style":5483},[823],[578,5506,5508,5511],{"style":5507},"top:-3.063em;margin-right:0.05em;",[578,5509],{"className":5510,"style":1681},[831],[578,5512,5514],{"className":5513},[1685,1686,1687,1688],[578,5515,2564],{"className":5516},[908,1688]," 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