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

Question

sirm3d · Answer

$$\sin^2 x + \sin^2 y=1$$
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.