Question

помогите пожалуйста!!!

Answer 1

$2\, sin\Big(\dfrac{\pi}{4}+\dfrac{x}{5}\Big)=\sqrt3\\\\\\sin\Big(\dfrac{\pi}{4}+\dfrac{x}{5}\Big)=\dfrac{\sqrt3}{2}\\\\\\\Big(\dfrac{\pi}{4}+\dfrac{x}{5}\Big)=(-1)^{k}\cdot \dfrac{\pi}{3}+\pi k\ ,\ k\in Z\\\\\\\dfrac{x}{5}=-\dfrac{\pi}{4}+(-1)^{k}\cdot \dfrac{\pi}{3}+\pi k\ ,\ k\in Z\\\\\\x=-\dfrac{5\pi }{4}+(-1)^{k}\cdot \dfrac{5\pi}{3}+5\pi k\ ,\ k\in Z$