# Find a functional relationship between $u$ and $v$

Let $u=\sin^{-1}x+\sin^{-1}y$ and $v=x\sqrt{1-y^2}+y\sqrt{1-x^2}$. Determine whether there is a functional relationship between $u$ and $v$.

I did some handy calculations but they are useless. Please help me to find the relation. Thank you very much!

Let $\arcsin(x) = a$ and $\arcsin(y) = b$. Hence, $x = \sin(a)$ and $y = \sin(b)$. We then have $$u=a+b$$ and $$v = \sin(a)\cos(b) + \sin(b) \cos(a) = \sin(a+b)$$ Hence, we get that $$v = \sin(u)$$