Question

cos 2x + sin^2 x = 1

Answer 1

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