Решите уравнение sqrt(3)(sin^2 x tg x + cos^2 x ctg x) = 4 - sqrt(3)sin 2x .

Задача №17714: Уравнение

3 (sin^{2} x t g x + cos^{2} x ct g x) = 4 - 3 sin 2 x ⟺ \frac{sin ^{4} x + cos ^{4} x}{sin x cos x} = \frac{4}{3} - 2 sin x cos x ⟺

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

⟺ sin 2 x = \frac{3}{2} ⟺ 2 x = \frac{π}{3} + 2 k π, \frac{2 π}{3} + 2 k π, k \in Z ⟺ x = \frac{π}{6} + k π, \frac{π}{3} + k π, k \in Z