Question

Cos(2x) + sin^2(x) = 0

Answer 1

cos(2θ) + sin²(θ) = 0

Half-angle identity:

cos(2θ) + (1 - cos(2θ))/2 = 0

Simplify:

2 cos(2θ) + 1 - cos(2θ) = 0

cos(2θ) = -1

Solve for θ :

2θ = arccos(-1) + 2nπ

2θ = π + 2nπ

θ = π/2 + nπ

where n is any integer.