5 sin4x = 6 cos^2x.

2Sin 2x Cos 2x = 6Cos² 2x - 4 (Sin² 2x + Cos²2x)

2Sin 2x Cos 2x - 6Cos² 2x + 4Sin² 2x + 4Cos²2x = 0

2Sin 2x Cos 2x - 2Cos² 2x + 4 Sin² 2x = 0 | : Сos²2x ≠ 0

2 tg 2x - 2 + 4tg² 2x = 0

2tg² 2x + tg x - 1 = 0

решаем как квадратное.

D = 9

tg 2x = (-1 + - 3) / 4

а) tg 2x = 1/2 б) tg 2x = - 1

2x = arctg 1/2 + πk, k∈Z 2x = arctg (-1) + πn, n∈Z

x = 1/2 arctg 1/2 + πk/2, k∈Z 2x = - π/4 + πn, n ∈Z

x = - π/8 + πn/2, n ∈Z