Question

Решите неравенство 2cos 2x ≥ 1
20 баллов

Answer 1

Ответ:

$2\, cos2x\geq 1\ \ \ \Rightarrow \ \ \ cos2x\geq \dfrac{1}{2}\ \ ,\\\\\\-\dfrac{\pi}{3}+2\pi n\leq 2x\leq \dfrac{\pi}{3}+2\pi n\ ,\ n\in Z\\\\\\\-\dfrac{\pi}{6}+\pi n\leq x\leq \dfrac{\pi}{6}+\pi n\ ,\ n\in Z\\\\\\x\in \Big(-\dfrac{\pi}{6}+\pi n\ ;\ \dfrac{\pi}{6}+\pi n\ \Big)\ ,\ n\in Z$