Answer
$\sqrt {1 - x^{2} }$
Work Step by Step
Given expression is-
$\cos(\sin^{-1}x)$
Assuming $\sin^{-1} x$ = $u$ , we get-
$\sin u$ = $x$, [$-\frac{\pi}{2}\leq u\leq \frac{\pi}{2}$]
From First Pythagorean identity-
$\cos u$ = + $\sqrt {1 - \sin^{2} u}$
$\cos u$ = + $\sqrt {1 - x^{2} }$
i.e. $\cos(\sin^{-1}x)$ = $\sqrt {1 - x^{2} }$
