Задача №17616: Уравнение

Решите уравнение

cos 3 x + 2 sin 2 x + 2 cos x = 0.

cos 3 x + 2 sin 2 x + 2 cos x = 0 ⟺ cos 2 x cos x - sin 2 x sin x + 4 sin x cos x + 2 cos x = 0 ⟺

⟺ cos x (cos 2 x - 2 sin^{2} x + 4 sin x + 2) = 0 ⟺ cos x (3 - 4 sin^{2} x + 4 sin x) = 0 ⟺

⟺ cos x (sin^{2} x - sin x - \frac{3}{4}) = 0 ⟺ cos x (sin x + \frac{1}{2}) (sin x - \frac{3}{2}) = 0 ⟺

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

Решите уравнение

cos 3 x + 2 sin 2 x + 2 cos x = 0.

cos 3 x + 2 sin 2 x + 2 cos x = 0 ⟺ cos 2 x cos x - sin 2 x sin x + 4 sin x cos x + 2 cos x = 0 ⟺

⟺ cos x (cos 2 x - 2 sin^{2} x + 4 sin x + 2) = 0 ⟺ cos x (3 - 4 sin^{2} x + 4 sin x) = 0 ⟺

⟺ cos x (sin^{2} x - sin x - \frac{3}{4}) = 0 ⟺ cos x (sin x + \frac{1}{2}) (sin x - \frac{3}{2}) = 0 ⟺

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

Задача №17616