Question

Найдите значение выражения

Answer 1

$(sin\frac{5\pi }{4}-cos\frac{3\pi}{4})\cdot tg\frac{7\pi }{3}=(sin(\pi +\frac{\pi}{4})-cos(\pi -\frac{\pi}{4}))\cdot tg(2\pi -\frac{\pi}{4})=\\\\=(-sin\frac{\pi}{4}+cos\frac{\pi}{4})\cdot tg(-\frac{\pi}{4})=(-\frac{\sqrt2}{2}+\frac{\sqrt2}{2})\cdot (-1)=0$