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y}{2}",[578,1584,1586,1611,1635],{"className":1585,"ariaHidden":625},[624],[578,1587,1589,1593,1596,1599,1602,1605,1608],{"className":1588},[629],[578,1590],{"className":1591,"style":1592},[633],"height:0.6667em;vertical-align:-0.0833em;",[578,1594,964],{"className":1595},[995],[578,1597],{"className":1598,"style":1000},[999],[578,1600,604],{"className":1601},[638,708],[578,1603],{"className":1604,"style":1007},[999],[578,1606,608],{"className":1607},[712],[578,1609],{"className":1610,"style":1007},[999],[578,1612,1614,1617,1620,1623,1626,1629,1632],{"className":1613},[629],[578,1615],{"className":1616,"style":903},[633],[578,1618,964],{"className":1619},[995],[578,1621],{"className":1622,"style":1000},[999],[578,1624,611],{"className":1625,"style":716},[638,708],[578,1627],{"className":1628,"style":1033},[999],[578,1630,943],{"className":1631},[1037],[578,1633],{"className":1634,"style":1033},[999],[578,1636,1638,1641,1644,1647,1650,1653,1727,1730,1733,1736],{"className":1637},[629],[578,1639],{"className":1640,"style":1047},[633],[578,1642,615],{"className":1643},[638],[578,1645],{"className":1646,"style":1000},[999],[578,1648,964],{"className":1649},[995],[578,1651],{"className":1652,"style":1000},[999],[578,1654,1656,1659,1724],{"className":1655},[638],[578,1657],{"className":1658},[642,643],[578,1660,1662],{"className":1661},[597],[578,1663,1665,1716],{"className":1664},[650,651],[578,1666,1668,1713],{"className":1667},[655],[578,1669,1671,1682,1690],{"className":1670,"style":1078},[659],[578,1672,1673,1676],{"style":1081},[578,1674],{"className":1675,"style":668},[667],[578,1677,1679],{"className":1678},[638],[578,1680,615],{"className":1681},[638],[578,1683,1684,1687],{"style":684},[578,1685],{"className":1686,"style":668},[667],[578,1688],{"className":1689,"style":692},[691],[578,1691,1692,1695],{"style":1101},[578,1693],{"className":1694,"style":668},[667],[578,1696,1698,1701,1704,1707,1710],{"className":1697},[638],[578,1699,604],{"className":1700},[638,708],[578,1702],{"className":1703,"style":1007},[999],[578,1705,608],{"className":1706},[712],[578,1708],{"className":1709,"style":1007},[999],[578,1711,611],{"className":1712,"style":716},[638,708],[578,1714,721],{"className":1715},[720],[578,1717,1719],{"className":1718},[655],[578,1720,1722],{"className":1721,"style":1132},[659],[578,1723],{},[578,1725],{"className":1726},[734,643],[578,1728],{"className":1729,"style":1000},[999],[578,1731,964],{"className":1732},[995],[578,1734],{"className":1735,"style":1000},[999],[578,1737,1739,1742,1807],{"className":1738},[638],[578,1740],{"className":1741},[642,643],[578,1743,1745],{"className":1744},[597],[578,1746,1748,1799],{"className":1747},[650,651],[578,1749,1751,1796],{"className":1750},[655],[578,1752,1754,1765,1773],{"className":1753,"style":1078},[659],[578,1755,1756,1759],{"style":1081},[578,1757],{"className":1758,"style":668},[667],[578,1760,1762],{"className":1761},[638],[578,1763,615],{"className":1764},[638],[578,1766,1767,1770],{"style":684},[578,1768],{"className":1769,"style":668},[667],[578,1771],{"className":1772,"style":692},[691],[578,1774,1775,1778],{"style":1101},[578,1776],{"className":1777,"style":668},[667],[578,1779,1781,1784,1787,1790,1793],{"className":1780},[638],[578,1782,604],{"className":1783},[638,708],[578,1785],{"className":1786,"style":1007},[999],[578,1788,756],{"className":1789},[712],[578,1791],{"className":1792,"style":1007},[999],[578,1794,611],{"className":1795,"style":716},[638,708],[578,1797,721],{"className":1798},[720],[578,1800,1802],{"className":1801},[655],[578,1803,1805],{"className":1804,"style":1132},[659],[578,1806],{},[578,1808],{"className":1809},[734,643],[578,1811,1813],{"className":1812},[911],[578,1814,1816,1880],{"className":1815},[581],[578,1817,1819],{"className":1818},[585],[587,1820,1821],{"xmlns":589,"display":920},[591,1822,1823,1877],{},[594,1824,1825,1827,1829,1831,1833,1835,1837,1839,1841,1843,1845,1847,1849,1861,1863,1865],{},[602,1826,964],{},[606,1828,930],{},[602,1830,604],{},[606,1832,756],{},[602,1834,964],{},[606,1836,930],{},[602,1838,611],{},[606,1840,943],{},[606,1842,756],{},[613,1844,615],{},[602,1846,927],{},[606,1848,930],{},[597,1850,1851,1859],{},[594,1852,1853,1855,1857],{},[602,1854,604],{},[606,1856,608],{},[602,1858,611],{},[613,1860,615],{},[602,1862,927],{},[606,1864,930],{},[597,1866,1867,1875],{},[594,1868,1869,1871,1873],{},[602,1870,604],{},[606,1872,756],{},[602,1874,611],{},[613,1876,615],{},[617,1878,1879],{"encoding":619},"\\cos x - \\cos y = -2 \\sin\\frac{x + y}{2} \\sin\\frac{x - y}{2}",[578,1881,1883,1907,1931],{"className":1882,"ariaHidden":625},[624],[578,1884,1886,1889,1892,1895,1898,1901,1904],{"className":1885},[629],[578,1887],{"className":1888,"style":1592},[633],[578,1890,964],{"className":1891},[995],[578,1893],{"className":1894,"style":1000},[999],[578,1896,604],{"className":1897},[638,708],[578,1899],{"className":1900,"style":1007},[999],[578,1902,756],{"className":1903},[712],[578,1905],{"className":1906,"style":1007},[999],[578,1908,1910,1913,1916,1919,1922,1925,1928],{"className":1909},[629],[578,1911],{"className":1912,"style":903},[633],[578,1914,964],{"className":1915},[995],[578,1917],{"className":1918,"style":1000},[999],[578,1920,611],{"className":1921,"style":716},[638,708],[578,1923],{"className":1924,"style":1033},[999],[578,1926,943],{"className":1927},[1037],[578,1929],{"className":1930,"style":1033},[999],[578,1932,1934,1937,1940,1943,1946,1949,1952,2026,2029,2032,2035],{"className":1933},[629],[578,1935],{"className":1936,"style":1047},[633],[578,1938,756],{"className":1939},[638],[578,1941,615],{"className":1942},[638],[578,1944],{"className":1945,"style":1000},[999],[578,1947,927],{"className":1948},[995],[578,1950],{"className":1951,"style":1000},[999],[578,1953,1955,1958,2023],{"className":1954},[638],[578,1956],{"className":1957},[642,643],[578,1959,1961],{"className":1960},[597],[578,1962,1964,2015],{"className":1963},[650,651],[578,1965,1967,2012],{"className":1966},[655],[578,1968,1970,1981,1989],{"className":1969,"style":1078},[659],[578,1971,1972,1975],{"style":1081},[578,1973],{"className":1974,"style":668},[667],[578,1976,1978],{"className":1977},[638],[578,1979,615],{"className":1980},[638],[578,1982,1983,1986],{"style":684},[578,1984],{"className":1985,"style":668},[667],[578,1987],{"className":1988,"style":692},[691],[578,1990,1991,1994],{"style":1101},[578,1992],{"className":1993,"style":668},[667],[578,1995,1997,2000,2003,2006,2009],{"className":1996},[638],[578,1998,604],{"className":1999},[638,708],[578,2001],{"className":2002,"style":1007},[999],[578,2004,608],{"className":2005},[712],[578,2007],{"className":2008,"style":1007},[999],[578,2010,611],{"className":2011,"style":716},[638,708],[578,2013,721],{"className":2014},[720],[578,2016,2018],{"className":2017},[655],[578,2019,2021],{"className":2020,"style":1132},[659],[578,2022],{},[578,2024],{"className":2025},[734,643],[578,2027],{"className":2028,"style":1000},[999],[578,2030,927],{"className":2031},[995],[578,2033],{"className":2034,"style":1000},[999],[578,2036,2038,2041,2106],{"className":2037},[638],[578,2039],{"className":2040},[642,643],[578,2042,2044],{"className":2043},[597],[578,2045,2047,2098],{"className":2046},[650,651],[578,2048,2050,2095],{"className":2049},[655],[578,2051,2053,2064,2072],{"className":2052,"style":1078},[659],[578,2054,2055,2058],{"style":1081},[578,2056],{"className":2057,"style":668},[667],[578,2059,2061],{"className":2060},[638],[578,2062,615],{"className":2063},[638],[578,2065,2066,2069],{"style":684},[578,2067],{"className":2068,"style":668},[667],[578,2070],{"className":2071,"style":692},[691],[578,2073,2074,2077],{"style":1101},[578,2075],{"className":2076,"style":668},[667],[578,2078,2080,2083,2086,2089,2092],{"className":2079},[638],[578,2081,604],{"className":2082},[638,708],[578,2084],{"className":2085,"style":1007},[999],[578,2087,756],{"className":2088},[712],[578,2090],{"className":2091,"style":1007},[999],[578,2093,611],{"className":2094,"style":716},[638,708],[578,2096,721],{"className":2097},[720],[578,2099,2101],{"className":2100},[655],[578,2102,2104],{"className":2103,"style":1132},[659],[578,2105],{},[578,2107],{"className":2108},[734,643],[565,2110,2111],{},"Anwendungen:",[2113,2114,2115,2122,2127],"ul",{},[2116,2117,2118,2121],"li",{},[569,2119,2120],{},"Gleichungen lösen",": Eine Summe gleich null wird zu einem Produkt gleich null, dann hilft der Satz vom Nullprodukt.",[2116,2123,2124,2126],{},[569,2125,555],{}," in der Physik: Die Überlagerung zweier Schwingungen mit ähnlicher Frequenz ist eine schnelle Schwingung, deren Amplitude langsam schwankt.",[2116,2128,2129,2130,2236],{},"Ableitungen über den Differenzenquotienten, etwa ",[578,2131,2133,2171],{"className":2132},[581],[578,2134,2136],{"className":2135},[585],[587,2137,2138],{"xmlns":589},[591,2139,2140,2168],{},[594,2141,2142,2144,2146,2150,2152,2154,2157,2160,2162,2164,2166],{},[602,2143,927],{},[606,2145,930],{},[606,2147,2149],{"stretchy":2148},"false","(",[602,2151,604],{},[606,2153,608],{},[602,2155,2156],{},"h",[606,2158,2159],{"stretchy":2148},")",[606,2161,756],{},[602,2163,927],{},[606,2165,930],{},[602,2167,604],{},[617,2169,2170],{"encoding":619},"\\sin(x + h) - \\sin x",[578,2172,2174,2199,2220],{"className":2173,"ariaHidden":625},[624],[578,2175,2177,2181,2184,2187,2190,2193,2196],{"className":2176},[629],[578,2178],{"className":2179,"style":2180},[633],"height:1em;vertical-align:-0.25em;",[578,2182,927],{"className":2183},[995],[578,2185,2149],{"className":2186},[642],[578,2188,604],{"className":2189},[638,708],[578,2191],{"className":2192,"style":1007},[999],[578,2194,608],{"className":2195},[712],[578,2197],{"className":2198,"style":1007},[999],[578,2200,2202,2205,2208,2211,2214,2217],{"className":2201},[629],[578,2203],{"className":2204,"style":2180},[633],[578,2206,2156],{"className":2207},[638,708],[578,2209,2159],{"className":2210},[734],[578,2212],{"className":2213,"style":1007},[999],[578,2215,756],{"className":2216},[712],[578,2218],{"className":2219,"style":1007},[999],[578,2221,2223,2227,2230,2233],{"className":2222},[629],[578,2224],{"className":2225,"style":2226},[633],"height:0.6679em;",[578,2228,927],{"className":2229},[995],[578,2231],{"className":2232,"style":1000},[999],[578,2234,604],{"className":2235},[638,708],".",[560,2238,2240],{"id":2239},"herleitung","Herleitung",[565,2242,2243,2244,877,2377,2510,2511,877,2584,2657],{},"Man setzt ",[578,2245,2247,2276],{"className":2246},[581],[578,2248,2250],{"className":2249},[585],[587,2251,2252],{"xmlns":589},[591,2253,2254,2273],{},[594,2255,2256,2259,2261],{},[602,2257,2258],{},"u",[606,2260,943],{},[597,2262,2263,2271],{},[594,2264,2265,2267,2269],{},[602,2266,604],{},[606,2268,608],{},[602,2270,611],{},[613,2272,615],{},[617,2274,2275],{"encoding":619},"u = \\frac{x + y}{2}",[578,2277,2279,2297],{"className":2278,"ariaHidden":625},[624],[578,2280,2282,2285,2288,2291,2294],{"className":2281},[629],[578,2283],{"className":2284,"style":873},[633],[578,2286,2258],{"className":2287},[638,708],[578,2289],{"className":2290,"style":1033},[999],[578,2292,943],{"className":2293},[1037],[578,2295],{"className":2296,"style":1033},[999],[578,2298,2300,2303],{"className":2299},[629],[578,2301],{"className":2302,"style":634},[633],[578,2304,2306,2309,2374],{"className":2305},[638],[578,2307],{"className":2308},[642,643],[578,2310,2312],{"className":2311},[597],[578,2313,2315,2366],{"className":2314},[650,651],[578,2316,2318,2363],{"className":2317},[655],[578,2319,2321,2335,2343],{"className":2320,"style":660},[659],[578,2322,2323,2326],{"style":663},[578,2324],{"className":2325,"style":668},[667],[578,2327,2329],{"className":2328},[672,673,674,675],[578,2330,2332],{"className":2331},[638,675],[578,2333,615],{"className":2334},[638,675],[578,2336,2337,2340],{"style":684},[578,2338],{"className":2339,"style":668},[667],[578,2341],{"className":2342,"style":692},[691],[578,2344,2345,2348],{"style":695},[578,2346],{"className":2347,"style":668},[667],[578,2349,2351],{"className":2350},[672,673,674,675],[578,2352,2354,2357,2360],{"className":2353},[638,675],[578,2355,604],{"className":2356},[638,708,675],[578,2358,608],{"className":2359},[712,675],[578,2361,611],{"className":2362,"style":716},[638,708,675],[578,2364,721],{"className":2365},[720],[578,2367,2369],{"className":2368},[655],[578,2370,2372],{"className":2371,"style":728},[659],[578,2373],{},[578,2375],{"className":2376},[734,643],[578,2378,2380,2409],{"className":2379},[581],[578,2381,2383],{"className":2382},[585],[587,2384,2385],{"xmlns":589},[591,2386,2387,2406],{},[594,2388,2389,2392,2394],{},[602,2390,2391],{},"v",[606,2393,943],{},[597,2395,2396,2404],{},[594,2397,2398,2400,2402],{},[602,2399,604],{},[606,2401,756],{},[602,2403,611],{},[613,2405,615],{},[617,2407,2408],{"encoding":619},"v = \\frac{x - y}{2}",[578,2410,2412,2430],{"className":2411,"ariaHidden":625},[624],[578,2413,2415,2418,2421,2424,2427],{"className":2414},[629],[578,2416],{"className":2417,"style":873},[633],[578,2419,2391],{"className":2420,"style":716},[638,708],[578,2422],{"className":2423,"style":1033},[999],[578,2425,943],{"className":2426},[1037],[578,2428],{"className":2429,"style":1033},[999],[578,2431,2433,2436],{"className":2432},[629],[578,2434],{"className":2435,"style":634},[633],[578,2437,2439,2442,2507],{"className":2438},[638],[578,2440],{"className":2441},[642,643],[578,2443,2445],{"className":2444},[597],[578,2446,2448,2499],{"className":2447},[650,651],[578,2449,2451,2496],{"className":2450},[655],[578,2452,2454,2468,2476],{"className":2453,"style":660},[659],[578,2455,2456,2459],{"style":663},[578,2457],{"className":2458,"style":668},[667],[578,2460,2462],{"className":2461},[672,673,674,675],[578,2463,2465],{"className":2464},[638,675],[578,2466,615],{"className":2467},[638,675],[578,2469,2470,2473],{"style":684},[578,2471],{"className":2472,"style":668},[667],[578,2474],{"className":2475,"style":692},[691],[578,2477,2478,2481],{"style":695},[578,2479],{"className":2480,"style":668},[667],[578,2482,2484],{"className":2483},[672,673,674,675],[578,2485,2487,2490,2493],{"className":2486},[638,675],[578,2488,604],{"className":2489},[638,708,675],[578,2491,756],{"className":2492},[712,675],[578,2494,611],{"className":2495,"style":716},[638,708,675],[578,2497,721],{"className":2498},[720],[578,2500,2502],{"className":2501},[655],[578,2503,2505],{"className":2504,"style":728},[659],[578,2506],{},[578,2508],{"className":2509},[734,643],", also ",[578,2512,2514,2536],{"className":2513},[581],[578,2515,2517],{"className":2516},[585],[587,2518,2519],{"xmlns":589},[591,2520,2521,2533],{},[594,2522,2523,2525,2527,2529,2531],{},[602,2524,604],{},[606,2526,943],{},[602,2528,2258],{},[606,2530,608],{},[602,2532,2391],{},[617,2534,2535],{"encoding":619},"x = u + v",[578,2537,2539,2557,2575],{"className":2538,"ariaHidden":625},[624],[578,2540,2542,2545,2548,2551,2554],{"className":2541},[629],[578,2543],{"className":2544,"style":873},[633],[578,2546,604],{"className":2547},[638,708],[578,2549],{"className":2550,"style":1033},[999],[578,2552,943],{"className":2553},[1037],[578,2555],{"className":2556,"style":1033},[999],[578,2558,2560,2563,2566,2569,2572],{"className":2559},[629],[578,2561],{"className":2562,"style":1592},[633],[578,2564,2258],{"className":2565},[638,708],[578,2567],{"className":2568,"style":1007},[999],[578,2570,608],{"className":2571},[712],[578,2573],{"className":2574,"style":1007},[999],[578,2576,2578,2581],{"className":2577},[629],[578,2579],{"className":2580,"style":873},[633],[578,2582,2391],{"className":2583,"style":716},[638,708],[578,2585,2587,2609],{"className":2586},[581],[578,2588,2590],{"className":2589},[585],[587,2591,2592],{"xmlns":589},[591,2593,2594,2606],{},[594,2595,2596,2598,2600,2602,2604],{},[602,2597,611],{},[606,2599,943],{},[602,2601,2258],{},[606,2603,756],{},[602,2605,2391],{},[617,2607,2608],{"encoding":619},"y = u - v",[578,2610,2612,2630,2648],{"className":2611,"ariaHidden":625},[624],[578,2613,2615,2618,2621,2624,2627],{"className":2614},[629],[578,2616],{"className":2617,"style":903},[633],[578,2619,611],{"className":2620,"style":716},[638,708],[578,2622],{"className":2623,"style":1033},[999],[578,2625,943],{"className":2626},[1037],[578,2628],{"className":2629,"style":1033},[999],[578,2631,2633,2636,2639,2642,2645],{"className":2632},[629],[578,2634],{"className":2635,"style":1592},[633],[578,2637,2258],{"className":2638},[638,708],[578,2640],{"className":2641,"style":1007},[999],[578,2643,756],{"className":2644},[712],[578,2646],{"className":2647,"style":1007},[999],[578,2649,2651,2654],{"className":2650},[629],[578,2652],{"className":2653,"style":873},[633],[578,2655,2391],{"className":2656,"style":716},[638,708],". Mit den Additionstheoremen heben sich die gemischten Terme weg:",[578,2659,2661],{"className":2660},[911],[578,2662,2664,2722],{"className":2663},[581],[578,2665,2667],{"className":2666},[585],[587,2668,2669],{"xmlns":589,"display":920},[591,2670,2671,2719],{},[594,2672,2673,2675,2677,2679,2681,2683,2685,2687,2689,2691,2693,2695,2697,2699,2701,2703,2705,2707,2709,2711,2713,2715,2717],{},[602,2674,927],{},[606,2676,930],{},[606,2678,2149],{"stretchy":2148},[602,2680,2258],{},[606,2682,608],{},[602,2684,2391],{},[606,2686,2159],{"stretchy":2148},[606,2688,608],{},[602,2690,927],{},[606,2692,930],{},[606,2694,2149],{"stretchy":2148},[602,2696,2258],{},[606,2698,756],{},[602,2700,2391],{},[606,2702,2159],{"stretchy":2148},[606,2704,943],{},[613,2706,615],{},[602,2708,927],{},[606,2710,930],{},[602,2712,2258],{},[602,2714,964],{},[606,2716,930],{},[602,2718,2391],{},[617,2720,2721],{"encoding":619},"\\sin(u + v) + \\sin(u - v) = 2 \\sin u \\cos 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Mit ",[578,5767,5769,5795],{"className":5768},[581],[578,5770,5772],{"className":5771},[585],[587,5773,5774],{"xmlns":589},[591,5775,5776,5792],{},[594,5777,5778,5780,5782,5784,5786],{},[602,5779,604],{},[606,5781,943],{},[602,5783,611],{},[606,5785,943],{},[597,5787,5788,5790],{},[602,5789,4988],{},[613,5791,615],{},[617,5793,5794],{"encoding":619},"x = y = \\frac{\\pi}{2}",[578,5796,5798,5816,5834],{"className":5797,"ariaHidden":625},[624],[578,5799,5801,5804,5807,5810,5813],{"className":5800},[629],[578,5802],{"className":5803,"style":873},[633],[578,5805,604],{"className":5806},[638,708],[578,5808],{"className":5809,"style":1033},[999],[578,5811,943],{"className":5812},[1037],[578,5814],{"className":5815,"style":1033},[999],[578,5817,5819,5822,5825,5828,5831],{"className":5818},[629],[578,5820],{"className":5821,"style":903},[633],[578,5823,611],{"className":5824,"style":716},[638,708],[578,5826],{"className":5827,"style":1033},[999],[578,5829,943],{"className":5830},[1037],[578,5832],{"className":5833,"style":1033},[999],[578,5835,5837,5840],{"className":5836},[629],[578,5838],{"className":5839,"style":5041},[633],[578,5841,5843,5846,5905],{"className":5842},[638],[578,5844],{"className":5845},[642,643],[578,5847,5849],{"className":5848},[597],[578,5850,5852,5897],{"className":5851},[650,651],[578,5853,5855,5894],{"className":5854},[655],[578,5856,5858,5872,5880],{"className":5857,"style":5060},[659],[578,5859,5860,5863],{"style":663},[578,5861],{"className":5862,"style":668},[667],[578,5864,5866],{"className":5865},[672,673,674,675],[578,5867,5869],{"className":5868},[638,675],[578,5870,615],{"className":5871},[638,675],[578,5873,5874,5877],{"style":684},[578,5875],{"className":5876,"style":668},[667],[578,5878],{"className":5879,"style":692},[691],[578,5881,5882,5885],{"style":5085},[578,5883],{"className":5884,"style":668},[667],[578,5886,5888],{"className":5887},[672,673,674,675],[578,5889,5891],{"className":5890},[638,675],[578,5892,4988],{"className":5893,"style":716},[638,708,675],[578,5895,721],{"className":5896},[720],[578,5898,5900],{"className":5899},[655],[578,5901,5903],{"className":5902,"style":728},[659],[578,5904],{},[578,5906],{"className":5907},[734,643]," ist links ",[578,5910,5912,5925],{"className":5911},[581],[578,5913,5915],{"className":5914},[585],[587,5916,5917],{"xmlns":589},[591,5918,5919,5923],{},[594,5920,5921],{},[613,5922,615],{},[617,5924,615],{"encoding":619},[578,5926,5928],{"className":5927,"ariaHidden":625},[624],[578,5929,5931,5934],{"className":5930},[629],[578,5932],{"className":5933,"style":3576},[633],[578,5935,615],{"className":5936},[638],", rechts ",[578,5939,5941,5963],{"className":5940},[581],[578,5942,5944],{"className":5943},[585],[587,5945,5946],{"xmlns":589},[591,5947,5948,5960],{},[594,5949,5950,5952,5954,5956,5958],{},[602,5951,927],{},[606,5953,930],{},[602,5955,4988],{},[606,5957,943],{},[613,5959,3537],{},[617,5961,5962],{"encoding":619},"\\sin \\pi = 0",[578,5964,5966,5990],{"className":5965,"ariaHidden":625},[624],[578,5967,5969,5972,5975,5978,5981,5984,5987],{"className":5968},[629],[578,5970],{"className":5971,"style":2226},[633],[578,5973,927],{"className":5974},[995],[578,5976],{"className":5977,"style":1000},[999],[578,5979,4988],{"className":5980,"style":716},[638,708],[578,5982],{"className":5983,"style":1033},[999],[578,5985,943],{"className":5986},[1037],[578,5988],{"className":5989,"style":1033},[999],[578,5991,5993,5996],{"className":5992},[629],[578,5994],{"className":5995,"style":3576},[633],[578,5997,3537],{"className":5998},[638],[2116,6000,6001,6002,6073,6074,2236],{},"Das Minuszeichen bei ",[578,6003,6005,6031],{"className":6004},[581],[578,6006,6008],{"className":6007},[585],[587,6009,6010],{"xmlns":589},[591,6011,6012,6028],{},[594,6013,6014,6016,6018,6020,6022,6024,6026],{},[602,6015,964],{},[606,6017,930],{},[602,6019,604],{},[606,6021,756],{},[602,6023,964],{},[606,6025,930],{},[602,6027,611],{},[617,6029,6030],{"encoding":619},"\\cos x - \\cos y",[578,6032,6034,6058],{"className":6033,"ariaHidden":625},[624],[578,6035,6037,6040,6043,6046,6049,6052,6055],{"className":6036},[629],[578,6038],{"className":6039,"style":1592},[633],[578,6041,964],{"className":6042},[995],[578,6044],{"className":6045,"style":1000},[999],[578,6047,604],{"className":6048},[638,708],[578,6050],{"className":6051,"style":1007},[999],[578,6053,756],{"className":6054},[712],[578,6056],{"className":6057,"style":1007},[999],[578,6059,6061,6064,6067,6070],{"className":6060},[629],[578,6062],{"className":6063,"style":903},[633],[578,6065,964],{"className":6066},[995],[578,6068],{"className":6069,"style":1000},[999],[578,6071,611],{"className":6072,"style":716},[638,708]," vergessen. Nur diese Formel hat den Faktor ",[578,6075,6077,6093],{"className":6076},[581],[578,6078,6080],{"className":6079},[585],[587,6081,6082],{"xmlns":589},[591,6083,6084,6090],{},[594,6085,6086,6088],{},[606,6087,756],{},[613,6089,615],{},[617,6091,6092],{"encoding":619},"-2",[578,6094,6096],{"className":6095,"ariaHidden":625},[624],[578,6097,6099,6102,6105],{"className":6098},[629],[578,6100],{"className":6101,"style":4282},[633],[578,6103,756],{"className":6104},[638],[578,6106,615],{"className":6107},[638],[2116,6109,6110,6111,6226],{},"Die Halbierungen weglassen und ",[578,6112,6114,6154],{"className":6113},[581],[578,6115,6117],{"className":6116},[585],[587,6118,6119],{"xmlns":589},[591,6120,6121,6151],{},[594,6122,6123,6125,6127,6129,6131,6133,6135,6137,6139,6141,6143,6145,6147,6149],{},[602,6124,927],{},[606,6126,930],{},[606,6128,2149],{"stretchy":2148},[602,6130,604],{},[606,6132,608],{},[602,6134,611],{},[606,6136,2159],{"stretchy":2148},[602,6138,964],{},[606,6140,930],{},[606,6142,2149],{"stretchy":2148},[602,6144,604],{},[606,6146,756],{},[602,6148,611],{},[606,6150,2159],{"stretchy":2148},[617,6152,6153],{"encoding":619},"\\sin(x + y) \\cos(x - y)",[578,6155,6157,6181,6214],{"className":6156,"ariaHidden":625},[624],[578,6158,6160,6163,6166,6169,6172,6175,6178],{"className":6159},[629],[578,6161],{"className":6162,"style":2180},[633],[578,6164,927],{"className":6165},[995],[578,6167,2149],{"className":6168},[642],[578,6170,604],{"className":6171},[638,708],[578,6173],{"className":6174,"style":1007},[999],[578,6176,608],{"className":6177},[712],[578,6179],{"className":6180,"style":1007},[999],[578,6182,6184,6187,6190,6193,6196,6199,6202,6205,6208,6211],{"className":6183},[629],[578,6185],{"className":6186,"style":2180},[633],[578,6188,611],{"className":6189,"style":716},[638,708],[578,6191,2159],{"className":6192},[734],[578,6194],{"className":6195,"style":1000},[999],[578,6197,964],{"className":6198},[995],[578,6200,2149],{"className":6201},[642],[578,6203,604],{"className":6204},[638,708],[578,6206],{"className":6207,"style":1007},[999],[578,6209,756],{"className":6210},[712],[578,6212],{"className":6213,"style":1007},[999],[578,6215,6217,6220,6223],{"className":6216},[629],[578,6218],{"className":6219,"style":2180},[633],[578,6221,611],{"className":6222,"style":716},[638,708],[578,6224,2159],{"className":6225},[734]," schreiben.",{"title":6228,"searchDepth":6229,"depth":6229,"links":6230},"",2,[6231,6232,6233,6234],{"id":562,"depth":6229,"text":563},{"id":2239,"depth":6229,"text":2240},{"id":3241,"depth":6229,"text":3242},{"id":5583,"depth":6229,"text":5584},[6236,6239,6242,6245,6248,6251,6254,6257,6260,6263,6266,6268,6270],{"lhs":6237,"rhs":6238},"sin(x) + sin(y)","2*sin((x + y)\u002F2)*cos((x - y)\u002F2)",{"lhs":6240,"rhs":6241},"sin(x) - sin(y)","2*cos((x + y)\u002F2)*sin((x - y)\u002F2)",{"lhs":6243,"rhs":6244},"cos(x) + cos(y)","2*cos((x + y)\u002F2)*cos((x - y)\u002F2)",{"lhs":6246,"rhs":6247},"cos(x) - cos(y)","-2*sin((x + y)\u002F2)*sin((x - y)\u002F2)",{"lhs":6249,"rhs":6250},"sin(u + v) + sin(u - v)","2*sin(u)*cos(v)",{"lhs":6252,"rhs":6253},"sin(75*pi\u002F180) + sin(15*pi\u002F180)","2*sin(45*pi\u002F180)*cos(30*pi\u002F180)",{"lhs":6255,"rhs":6256},"2*sqrt(2)\u002F2*sqrt(3)\u002F2","sqrt(6)\u002F2",{"lhs":6258,"rhs":6259},"cos(75*pi\u002F180) - cos(15*pi\u002F180)","-2*sin(45*pi\u002F180)*sin(30*pi\u002F180)",{"lhs":6261,"rhs":6262},"-2*sqrt(2)\u002F2*1\u002F2","-sqrt(2)\u002F2",{"lhs":6264,"rhs":6265},"sin(3*x) + sin(x)","2*sin(2*x)*cos(x)",{"lhs":6267,"rhs":3537},"sin(3*pi\u002F2) + sin(pi\u002F2)",{"lhs":6269,"rhs":615},"sin(pi\u002F2) + sin(pi\u002F2)",{"lhs":6271,"rhs":3537},"sin(pi)",null,"md","sum-to-product","\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>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sin x + \\sin y = 2 \\sin\\frac{x + y}{2} \\cos\\frac{x - y}{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:0.7512em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:0.8623em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\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:1.9463em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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:1.2603em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\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 mathnormal\">x\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=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\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:0.686em;\">\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:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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:1.2603em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\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 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