Question

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

Answer 1

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