Решите уравнение sin 2x + 3cos x = sqrt(3)(1 + cos 2x + sin x) .

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

\( x = \pm\frac{\pi}{6} + 2k\pi,\ \frac{\pi}{3} + k\pi,\ k \in \mathbb{Z} \)