Решите уравнение cos 4x + cos 2x + ctg^2 x = 0 .

cos 4x + cos 2x + ctg^2 x = 0 2cos^2 2x + cos 2x + (cos 2x)/(sin^2 x) = 0 cos 2x ( 2 - 4sin^2 x + 1 + (1)/(sin^2 x) ) = 0 (cos 2x)/(sin^2 x) ( 4sin^4 x - 3sin^2 x - 1 ) = 0 (cos 2x (sin^2 x - 1)(4sin^2 x + 1))/(sin^2 x) = 0 cases [ arrayl cos 2x = 0 sin x = +- 1 array . sin x != 0 cases [ arrayl x = (pi)/(4) + (kpi)/(2) x = (pi)/(2) + kpi array ., k in Z

\( x = \pi/2 + k\pi, \ \pi/4 + k\pi/2, \ k \in \mathbb{Z} \)