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

Задача №17496: Уравнение

tg 2 x = 2 cos 2 x ctg x ⟺ {sin x cos 2 x \neq = 0 sin x sin 2 x = 2 cos^{2} 2 x cos x ⟺

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

⟺ {sin x cos 2 x \neq = 0 cos x (2 cos 2 x - 1) (cos 2 x + 1) = 0 ⟺ x = \pm π /6 + k π, π /2 + k π, k \in Z