Question

Решить неравенство. Cоs(2х+П/3)> -Корень из 3/2

Answer 1

$\cos \Big(2x+\dfrac{\pi}{3}\Big)>-\dfrac{\sqrt{3}}{2}\\ \\ -\dfrac{5\pi}{6}+2\pi n <2x+\dfrac{\pi}{3}<\dfrac{5\pi}{6}+2\pi n,n \in \mathbb{Z}~~~~\bigg|-\dfrac{\pi}{3}\\ \\ -\dfrac{7\pi}{6}+2\pi n <2x<\dfrac{\pi}{2}+2\pi n , n \in \mathbb{Z}~~~~\bigg|:2\\ \\ \boxed{-\dfrac{7\pi}{12}+\pi n<x<\dfrac{\pi}{4}+\pi n,n \in \mathbb{Z}}$