Решите уравнение cos 2x + 6sin 2x = cos 4x + 6sin x .

cos 2x + 6sin 2x = cos 4x + 6sin x -2sin^2 x + 6sin 2x = -2sin^2 2x + 6sin x sin^2 2x - sin^2 x = 3(sin x - sin 2x) (sin x - sin 2x)(sin x + sin 2x + 3) = 0 sin x - sin 2x = 0 sin x (1 - 2cos x) = 0 [ arrayl sin x = 0 cos x = 1/2 array . [ arrayl x = kpi x = +-pi/3 + 2kpi array ., k in Z.

x = k\pi,\ \pm\pi/3 + 2k\pi,\ k \in \mathbb{Z}