Помогите с тригонометрическим уравнением sin^2x-2cosx+2=0

1 - cos^2x - 2cosx + 2 = 0

- cos^2x - 2cosx + 3 = 0 / : (-1)

cos^2x + 2cosx - 3 = 0

cosx = t, | t | ≤ 1

t^2 + 2t - 3 = 0

D = 4 + 12 = 16

t1 = (- 2 + 4) / 2 = 2/2 = 1 ∈ t

t2 = (- 2 - 4) / 2 = - 6/2 = - 3 ∉ t

cosx = 1

x = 2pik, k ∈ Z