Answer
$\frac{\sqrt{x^2-1}}{x}$
Work Step by Step
Let $\sin ^ {–1} \frac{1}{x} = \theta$
then, $\sin \theta = \frac{1}{x}$
To evaluate $\cos (\sin ^ {–1} \frac{1}{x}) = \cos \theta$
We know that, $\cos \theta = \sqrt{1 - \sin ^2 \theta}$
Using above relations we get
$\cos \theta = \sqrt{1-\frac{1}{x^2}}$
$=> \cos \theta = \frac{\sqrt{x^2-1}}{x}$
