Answer
$sec\left( \sin ^{-1}x\right) =\dfrac {1}{\sqrt {1-x^{2}}}$
Work Step by Step
Lets assume that
$\sin ^{-1}x=\alpha \Rightarrow \sin \alpha =x$
$sec\left( \sin ^{-1}x\right) =sec\alpha =\dfrac {1}{\cos \alpha }=\dfrac {1}{\sqrt {1-\sin ^{2}\alpha }}=\dfrac {1}{\sqrt {1-x^{2}}}$
