Answer
$x$
Work Step by Step
We are given the expression: $\sin (\sin^{-1} x)$
$y=\sin^{-1} x$ is the value of $y$ so that $\sin y=x$, where $-\dfrac{\pi}{2}\leq y\leq \dfrac{\pi}{2}$.
For $y\in\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$, we have:
$f^{-1}(f(x))=x$; $f(f^{-1})(y)=y$
$\sin(\sin^{-1}(x))=x$, where $x\in[-1,1]$
So we get:
$\sin(\sin^{-1} x)=x$
