If $\sin^{-1} x + \sin^{-1} y = \pi$, what is $x + y$?

Explanation

1. 01

   Each principal value is at most $\frac{\pi}{2}$, so a sum of $\pi$ needs both to be $\frac{\pi}{2}$.

2. 02

   So $x = y = 1$ and $x + y = 2$.