3 sin квадрат x - 4 sin x cos x + 5 cos квадрат x = 2

Помогите решить

3sin^2x - 4sinxcosx + 5cos^2x = 2*1

3sin^2x - 4sinxcosx + 5cos^2x = 2 * (sin^2x+cos^2x)

3sin^2x - 4sinxcosx + 5cos^2x = 2sin^2x + 2cos^2x

3sin^2x - 2sin^2x - 4sinx*cosx + 5cos^2x - 2cos^2x = 0

sin^2x - 4sinx*cosx + 3cos^2x = 0 / / : cos^2x ≠ 0

tg^2x - 4tgx + 3 = 0

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

tgx = 3

x = arctg (3) + pik, k ∈Z

tgx = 1

x = pi/4 + pik, k ∈Z