Question

Решите неравенство cos^2x ≥0,25

Answer 1

$\cos^2x\geq 0{,}25\\ \\ \dfrac{1+\cos2x}{2}\geq 0{,}25\\ \\ 1+\cos2x\geq 0{,}5\\ \\ \cos 2x\geq -0{,}5\\ \\ -\dfrac{2\pi}{3}+2\pi n\leq 2x\leq \dfrac{2\pi}{3}+2\pi n,n \in \mathbb{Z}\\ \\ \boxed{-\dfrac{\pi}{3}+\pi n\leq x\leq \dfrac{\pi}{3}+\pi n,n \in \mathbb{Z}}$