Решите уравнение 9tg^2 x - 2cos 2x = 2 .

9tg^2 x - 2cos 2x = 2 (9)/(cos^2 x) - 9 - 2(2cos^2 x - 1) = 2 4cos^4 x + 9cos^2 x - 9 = 0 (4cos^2 x - 3)(cos^2 x + 3) = 0 cos x = +-sqrt(3)/2 x = +-pi/6 + kpi, k in Z.

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