Решите уравнение 4sin 2x cos 3x - 2sin 5x = tg 2x .

4sin 2x cos 3x - 2sin 5x = tg 2x 2sin 2x cos 3x - 2cos 2x sin 3x = tg 2x -2sin x = tg 2x (sin x (2cos 2x + 2cos x))/(cos 2x) = 0 (sin x (2cos^2 x + cos x - 1))/(cos 2x) = 0 (sin x (2cos x - 1)(cos x + 1))/(cos 2x) = 0 cases [ arrayl sin x = 0 cos x = -1 cos x = 1/2 array . cos 2x != 0 cases [ arrayl x = kpi x = +-pi/3 + 2kpi array ., k in Z

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