Question

Помогите пожалуйста срочно решение на листочке плис

Answer 1

$1)\ \ cos(2x+\dfrac{\pi}{6})<-\dfrac{\sqrt3}{2}\\\\\dfrac{5\pi}{6}+2\pi n<2x+\dfrac{\pi}{6}<\dfrac{7\pi }{6}+2\pi n\ ,\ n\in Z\\\\\dfrac{4\pi }{6}+2\pi n<2x<\dfrac{6\pi}{6}+2\pi n\ ,\ n\in Z\\\\\dfrac{2\pi}{3}+2\pi n<2x<\pi +2\pi n\ ,\ n\in Z\\\\\dfrac{\pi }{3}+\pi n<x<\dfrac{\pi}{2} +\pi n\ ,\ n\in Z$

$2)\ \ \sqrt2\, sin\Big (\dfrac{\pi }{4}+\dfrac{x}{2}\Big)<1\\\\sin\Big(\dfrac{\pi}{4}+\dfrac{x}{2}\Big)<\dfrac{1}{\sqrt2}\\\\\dfrac{3\pi }{4}+2\pi n<\dfrac{\pi}{4}+\dfrac{x}{2}<\dfrac{9\pi }{4}+2\pi n\ ,\ n\in Z$

$\dfrac{\pi}{2}+2\pi n<\dfrac{x}{2}<2\pi +2\pi n\ ,\ n\in Z\\\\\pi +4\pi n<x<4\pi +4\pi n\ ,\ n\in Z$