Решите уравнение (1)/(cos^2 x) + (12)/(sin^2 2x) + (12)/(sin x sin 2x) = (3)/(sin^2 x) .

(1)/(cos^2 x) + (12)/(sin^2 2x) + (12)/(sin x sin 2x) = (3)/(sin^2 x) (sin^2 x + 3 + 6cos x - 3cos^2 x)/(sin^2 x cos^2 x) = 0 (4 + 6cos x - 4cos^2 x)/(sin^2 x cos^2 x) = 0 (2(2 - cos x)(1 + 2cos x))/(sin^2 x cos^2 x) = 0 cos x = -(1)/(2) x = +-(2pi)/(3) + 2kpi, k in Z

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