Question

Помогите с алгеброй 10 класс триганометрия)

Answer 1

$Sin(\pi -2x)+Sin6x=3Cos^{2}2x\\\\Sin2x+Sin6x=3Cos^{2}2x\\\\2Sin\frac{2+6x}{2}Cos\frac{6x-2x}{2}=2Cos^{2}2x\\\\2Sin4xCos2x-3Cos^{2}2x=0\\\\Cos2x(2Sin4x-3Cos2x)=0\\\\Cos2x(4Sin2xCos2x-3Cos2x)=0\\\\Cos2xCos2x(4Sin2x-3)=0\\\\1)Cos2x=0\\\\2x=\frac{\pi }{2}+\pi n,n\in Z\\\\x=\frac{\pi }{4}+\frac{\pi n }{2},n\in Z\\\\2)4Sin2x-3=0\\\\Sin2x=\frac{3}{4}\\\\2x=(-1)^{n}arcSin\frac{3}{4}+\pi n,n\in Z\\\\x=(-1)^{n}\frac{1}{2}arcSin\frac{3}{4}+\frac{\pi n }{2},n\in Z$