Answer
$$\frac{{\sqrt {4 - {x^2}} }}{2}$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle shown bellow we have that}} \cr
& \tan \theta = \frac{{{\text{Opposite side}}}}{{{\text{Adjacent side}}}} \cr
& \tan \theta = \frac{{\sqrt {4 - {x^2}} }}{2} \cr
& and \cr
& {\text{sec}}\theta = \frac{x}{2} \cr
& \theta = {\sec ^{ - 1}}\left( {\frac{x}{2}} \right) \cr
& \cr
& {\text{Then,}} \cr
& \tan \theta = \tan \left( {{{\sec }^{ - 1}}\left( {\frac{x}{2}} \right)} \right) \cr
& \tan \theta = \frac{{\sqrt {4 - {x^2}} }}{2} \cr} $$
