3cos²x-2,5sin2x-2sin²x=0

3cos²x - 2,5sin2x - 2sin²x = 0

Разложим sin2x.

3cos²x - 5sinxcosx - 2sin²x = 0

Разделим на cos²x (cosx ≠ 0).

3 - 5tgx - 2tg² = 0

2tg²x + 5tgx - 3 = 0

Пусть t = tgx.

2t² + 5t - 3 = 0

D = 25 + 3•4•2 = 49 = 7².

t = (-5 + 7) / 4 = 1/2

t = (-5 - 7) / 4 = - 12/4 = - 3

Обратная замена:

tgx = 1/2

x = arctg (1/2) + πn, n ∈ Z

tgx = - 3

x = arctg (-3) + πn, n ∈ Z.