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

Задача №17580: Уравнение

cos 2 x + 6 sin 2 x = cos 4 x + 6 sin x ⟺ - 2 sin^{2} x + 6 sin 2 x = - 2 sin^{2} 2 x + 6 sin x ⟺ sin^{2} 2 x - sin^{2} x = 3 (sin x - sin 2 x) ⟺ (sin x - sin 2 x) (sin x + sin 2 x + 3) = 0 ⟺ sin x - sin 2 x = 0 ⟺ sin x (1 - 2 cos x) = 0 ⟺ [sin x = 0 cos x = 1/2 ⟺ [x = k π x = \pm π /3 + 2 k π, k \in Z .