Найдите занчение выражения sin51π6⋅sin31π6\sin\frac{51\pi}{6}\cdot \sin\frac{31\pi}{6}sin651π⋅sin631π▸Ответ-0,5▸Решениеsin51π6=sin(48π6+3π6)=\sin\frac{51\pi}{6}=\sin\left(\frac{48\pi}{6}+\frac{3\pi}{6}\right)=sin651π=sin(648π+63π)=sin(8π+π2)=sinπ2=1\sin\left(8\pi+\frac{\pi}{2}\right)=\sin\frac{\pi}{2}=1sin(8π+2π)=sin2π=1 sin31π6=sin(30π6+π6)=\sin\frac{31\pi}{6}=\sin\left(\frac{30\pi}{6}+\frac{\pi}{6}\right)=sin631π=sin(630π+6π)=sin(5π+π6)=−sinπ6=−12\sin\left(5\pi+\frac{\pi}{6}\right)=-\sin\frac{\pi}{6}=-\frac{1}{2}sin(5π+6π)=−sin6π=−21 sin51π6⋅sin31π6=\sin\frac{51\pi}{6}\cdot \sin\frac{31\pi}{6}=sin651π⋅sin631π=1⋅(−12)=−0,51\cdot \left(-\frac{1}{2}\right)=-0,51⋅(−21)=−0,5