Question

2 cosп/6*sin(x-п/6)=-√3 решите пожалуйста.

Answer 1

$2cdot cosfrac{pi}{6}cdot sin(x-frac{pi}{6})=-sqrt3\\2cdot frac{sqrt3}{2}cdot sin(x-frac{pi}{6})=-sqrt3\\sin(x-frac{pi}{6})=-1\\x-frac{pi}{6}=-frac{pi}{2}+2pi n; ,; nin Z\\x=frac{pi}{6}-frac{pi}{2}+2pi n; ,; nin Z\\x=-frac{pi}{3}+2pi n; ,; nin Z$