Question

cos(4x) - cos(2x) = 2sin(x)

Answer 1

cos4x - cos2x = 2sinx

cos(3x+x)-cos(3x-x) = 2sinx

-2sin(3x)sinx - 2sinx = 0

sin(x)(sin3x+1) = 0

sinx = 0  или  sin3x = -1

$\displaystyle x=\pi n\; \bigcup 3x=\frac{3\pi }2+2\pi k,\; n,k\in \mathbb{Z}$

Ответ: $\displaystyle x=\{ \pi n; \frac{\pi }2+\frac{2\pi k}3\} ,\; n,k\in \mathbb{Z}$