Решите уравнение ctg x - 2ctg 2x = (2)/(3)cos x .

ctg x - 2ctg 2x = (2)/(3)cos x (cos x)/(sin x) - (cos 2x)/(sin x cos x) = (2)/(3)cos x (sin^2 x)/(sin x cos x) = (2)/(3)cos x cases 3sin x = 2cos^2 x sin 2x != 0 cases cases 2sin^2 x + 3sin x - 2 = 0 sin 2x != 0 cases cases (2sin x - 1)(sin x + 2) = 0 sin 2x != 0 cases sin x = (1)/(2) x = (pi)/(6) + 2kpi, (5pi)/(6) + 2kpi, k in Z

\( x = \pi/6 + 2k\pi, \ 5\pi/6 + 2k\pi, \ k \in \mathbb{Z} \)