Question

How do i verify sin^2(pi/2-x) +sin^2x=1

Answer 1

\[\sin ^{2}(\frac{ \pi }{ 2 }-x)+\sin^2x=(\sin(\frac{ \pi }{ 2 }-x))^2+\sin^2x=(cosx)^2+\sin^2x=\cos^2x+\sin^2x\]

And as you should know, cos^2(x) + sin^2(x) is one of the Pythagorean identities, and is equivalent to 1.