Answer
$$\cot \theta = \frac{{\sqrt {4 - {x^2}} }}{x}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}x = 2\sin \theta ,{\text{ then }} \cr
& \sin \theta = \frac{x}{2} = \frac{{{\text{Opposite side}}}}{{{\text{Hypotenuse}}}} \cr
& {\text{Adjacent side}} = \sqrt {{2^2} - {x^2}} = \sqrt {4 - {x^2}} \cr
& \cr
& {\text{Express }}\cot \theta {\text{ in terms of }}x \cr
& \cot \theta = \frac{{{\text{Adjacent side}}}}{{{\text{Opposite side}}}} \cr
& \cot \theta = \frac{{\sqrt {4 - {x^2}} }}{x} \cr} $$
