Question

cos 2x + sin^2 x = 1

Answer 1

$\cos2x+\sin^2x=1\\ \\ \cos2x+\frac{1-\cos2x}{2} =1~~|\cdot 2\\ \\ 2\cos2x+1-\cos2x=2\\ \\ \cos2x=1\\\\ 2x=2 \pi n,n \in \mathbb{Z}\\ \\ x= \pi n,n \in \mathbb{Z}$