5-4 cos2 x = 5 sin2 x

5 - (4 - 8sin²x) = 10sinxcosx

1 + 8sin²x = 10sinxcosx

9sin²x + cos²x - 10sinxcosx = 0

9tg²x - 10tgx + 1 = 0

Пусть t = tgx.

9t² - 10t + 1 = 0

D = 100 - 36 = 64 = 8²

t1 = (10 + 8) / 18 = 1

t2 = (10 - 8) / 18 = 2/18 = 1/9.

Обратная замена:

tgx = 1

x = π/4 + 2πn, n ∈ Z.

tgx = 1/9

x = arctg (1/9) + πn, n ∈ Z.