Question

Write the given expression in terms of x and y only.
sin(sin^−1 (x) + cos^−1 (y))

Answer 1

sin(arcsin(x)) = x
sin(arccos(x)) = sqrt(1-x^2)

So...
\[\sin(\arcsin(x) + \arccos(y)) = x + \sqrt{1-y^2}\]
\[\sqrt{1-y^2} = -x \]
\[y = plus or minus \sqrt{1-x^2}\]