Найдите значение выражения 8sin44π3⋅cos35π68\sin\frac{44\pi}{3}\cdot\cos\frac{35\pi}{6}8sin344π⋅cos635π▸Ответ6▸Решениеsin44π3=sin(42π3+2π3)=\sin\frac{44\pi}{3}=\sin\left(\frac{42\pi}{3}+\frac{2\pi}{3}\right)=sin344π=sin(342π+32π)=sin(14π+2π3)=\sin\left(14\pi+\frac{2\pi}{3}\right)=sin(14π+32π)=sin2π3=32\sin\frac{2\pi}{3}=\frac{\sqrt{3}}{2}sin32π=23 cos35π6=cos(36π6−π6)=\cos\frac{35\pi}{6}=\cos\left(\frac{36\pi}{6}-\frac{\pi}{6}\right)=cos635π=cos(636π−6π)=cos(−π6)=cosπ6=32\cos\left(-\frac{\pi}{6}\right)=\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}cos(−6π)=cos6π=23 8sin44π3⋅cos35π6=8\sin\frac{44\pi}{3}\cdot\cos\frac{35\pi}{6}=8sin344π⋅cos635π=8⋅32⋅32=2⋅3=68\cdot \frac{\sqrt{3}}{2}\cdot \frac{\sqrt{3}}{2}=2\cdot 3=68⋅23⋅23=2⋅3=6