Question

Помогите, пожалуйста, решать неравенство

Answer 1

$3ctg(2x+\frac{\pi}{3} )\geq -\sqrt{3} \\ ctg(2x+\frac{\pi}{3} )\geq -\frac{1}{\sqrt{3}}\\ \\ \pi n\leq 2x+\frac{\pi}{3} \leq \frac{2\pi}{3} +\pi n,n\in \mathbb{Z}\\ \\ -\frac{\pi}{3} +\pi n\leq 2x\leq \frac{\pi}{3} +\pi n,n \in \mathbb{Z}\\ \\ \boxed{-\frac{\pi}{6}+\frac{\pi n}{2}\leq x\leq\frac{\pi}{6}+\frac{\pi n}{2},n \in \mathbb{Z} }$