Write the given expression in terms of x and y only.

sin (sin^-1 (x) + cos^-1 (y))

We are given the expression sin (sin-1 (X) + cos-1 (y)). We use the associative property to distribute the sine function. sin (sin-1 (x)) is equal to x. cos-1 (y) is equal to beta, the other angle besides alpha. sin beta is also equal to x which means the simplified term is 2x. This makes sense because sin-1 x = cos-1 y