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

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

\(x = \frac{\pi}{2} + k\pi,\ (-1)^k\frac{\pi}{6} + (k+1)\pi,\ k \in \mathbb{Z}\)