Question

4 sin(-7п/4) cos(-4п/3) ctg3п/4

Answer 1

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