Answer
$$\frac{{\sqrt {1 - {u^2}} }}{u}$$
Work Step by Step
$$\eqalign{
& \cot \left( {\arcsin u} \right) \cr
& {\text{From the triangle we have that}} \cr
& \sin \theta = u \cr
& \theta = \arcsin u \cr
& \cot \theta = \cot \left( {\arcsin u} \right) = \frac{{{\text{adjacent side}}}}{{{\text{opposite side}}}} \cr
& \cot \theta = \frac{{\sqrt {1 - {u^2}} }}{u} \cr} $$