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

sqrt(3)(sin^2 x tg x + cos^2 x ctg x) = 4 - sqrt(3)sin 2x (sin^4 x + cos^4 x)/(sin x cos x) = (4)/(sqrt(3)) - 2sin x cos x (sin^4 x + cos^4 x + 2sin^2 x cos^2 x)/(sin x cos x) = (4)/(sqrt(3)) (sin^2 x + cos^2 x)^2 = (2)/(sqrt(3))sin 2x sin 2x = (sqrt(3))/(2) 2x = (pi)/(3) + 2kpi, (2pi)/(3) + 2kpi, k in Z x = (pi)/(6) + kpi, (pi)/(3) + kpi, k in Z

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