Решите уравнение tg 2x = 2cos 2x ctg x .

tg 2x = 2cos 2x ctg x cases sin x cos 2x != 0 sin x sin 2x = 2cos^2 2x cos x cases cases sin x cos 2x != 0 cos x(2cos^2 2x - 2sin^2 x) = 0 cases cases sin x cos 2x != 0 cos x(2cos^2 2x + cos 2x - 1) = 0 cases cases sin x cos 2x != 0 cos x(2cos 2x - 1)(cos 2x + 1) = 0 cases x = +-pi/6 + kpi, pi/2 + kpi, k in Z

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