4sin2x+10cos^2x=1 помогите решить

4sin2x + 10cos²x = 1

8sinxcosx + 10cos²x = sin²x + cos²x

sin²x - 8sinxcosx - 9cos²x = 0 |:cos²x

tg²x - 8tgx - 9 = 0

tg²x - 8tgx + 16 - 25 = 0

(tgx - 4) ² - 5² = 0

(tgx - 4 - 1) (tgx - 4 + 5) = 0

(tgx - 5) (tgx + 1) = 0

tgx = 5 или tgx = - 1

x = arctg5 + πn, n ∈ Z

x = - π/4 + πn, n ∈ Z

Ответ: x = arctg5 + πn, n ∈ Z; x = - π/4 + πn, n ∈ Z.