Question

under which condition does sin squared x + sin squared y = 1? sorry im not sure how to type exponents on my computer

Answer 1

\[\sin^2 x + \sin^2 y=1\]
compare this with a known identity \[\sin^2 x + \cos^2 x =1\]

the logical solution is \[\sin^2 y=\cos^2 x\]

also, \[\sin y = \cos(\pi/2 - y)=\cos(y-\pi/2)\]

therefore \[\cos^2(\pi/2-y)=\cos^2 x=\cos^2(y-\pi/2)\]
one solution is given by \(\pi/2-y=x\) and another solution is \(y-\pi/2=x\)

there are solutions other than those i gave.