2cosx+cos^2 x=2-sin^2 x

2cosx+cos^2x=2-(1-cos^2x)
2cosx+cos^2x-2+1-cos^2x=0
2cosx=1
cosx=1/2
x₁=pi/3+2pi*n, n∈Z
x₂=-pi/3+2pi*n, n∈Z