2sin2x-sin^2x=3cos^2x

2sin2x - sin²x = 3cos²x

-sin²x + 4sinxcosx - 3cos²x = 0 |· (-1)

sin²x - 4sinxcosx + 3cos²x = 0 |:cos²x

tg²x - 4tgx + 3 = 0

tg²x - 4tgx + 4 - 1 = 0

(tg²x - 2) ² - 1² = 0

(tgx - 2 - 1) (tgx - 2 + 1) = 0

(tgx - 3) (tgx - 1) = 0

tgx = 3 или tgx = 3

x = arctg3 + πn, n ∈ Z или x = π/4 + πk, k ∈ Z

Ответ: x = x = π/4 + πk, k ∈ Z; arctg3 + πn, n ∈ Z.