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