Question

Помогите с тригонометрией(

Answer 1

$8tg\frac{7 \pi }{3}\cdot tg\frac{11 \pi }{6}=8tg(\frac{6 \pi }{3}+\frac{\pi }{3})\cdot tg(\frac{12 \pi}{6}-\frac{\pi }{6})=\\\ =8tg(2\pi+\frac{\pi }{3})\cdot tg(2 \pi-\frac{\pi }{6})=8tg\frac{\pi }{3}\cdot (-tg\frac{\pi }{6})=-8\sqrt3\cdot \frac{\sqrt3}{3}=-8$