Answer
$\frac{\sqrt{x^2-1}}{x}.$
Work Step by Step
Assume that $\sin\theta =\frac{x}{1}$, then by solving the triangle, we have:
$$\cot \theta=\frac{\sqrt{x^2-1}}{x}.$$
Now, since $\theta =\sin^{-1}x $, we have
$$\cot(\sin^{-1}x)=\cot\theta=\frac{\sqrt{x^2-1}}{x}.$$
