Question

$2 \cos(2x + \frac{\pi}{3} ) \geqslant 1$
помогите пожалуйста​

Answer 1

$2\cos\left ( 2x+\cfrac{\pi}{3} \right )\geq 1\Leftrightarrow \cos\left ( 2x+\cfrac{\pi}{3} \right )\geq \cfrac{1}{2}\Leftrightarrow \begin{cases}2x+\cfrac{\pi}{3}\leq \cfrac{\pi}{3}+2\pi k\\ 2x+\cfrac{\pi}{3}\geq -\cfrac{\pi}{3}+2\pi k\end{cases},k\in \mathbb{Z}$

$\begin{cases}x\leq \pi k\\ x\geq -\cfrac{\pi}{3}+\pi k\end{cases},k\in \mathbb{Z}\Rightarrow x\in \left [ -\cfrac{\pi}{3}+\pi k,\pi k \right ],k\in \mathbb{Z}$