Question

Помогите! С подробным решением!

Answer 1

$sin\frac{5\pi}{8}*sin\frac{7\pi}{8}*sin\frac{7\pi}{4}= \frac{cos(\frac{5\pi}{8}-\frac{7\pi}{8})-cos(\frac{5\pi}{8}+\frac{7\pi}{8})}{2}*(-\frac{\sqrt2}{2})=\\ =\frac{cos(-\frac{\pi}{4})-cos2\pi}{2}*(-\frac{\sqrt2}{2})=\frac{\frac{\sqrt2}{2}-1}{2}*(-\frac{\sqrt2}{2})=\\ =-\frac{1-\sqrt2}{4}=\frac{\sqrt2-1}{4}$