Answer
2 $|\sec\theta|$
Work Step by Step
Given expression-
$ \sqrt {x^{2} + 4}$
Substituting $2\tan\theta$ for $x$ as given, the expression becomes-
$ \sqrt {(2\tan\theta)^{2} + 4}$
= $ \sqrt {4\tan^{2}\theta + 4}$
= $ \sqrt {4(\tan^{2}\theta + 1)}$
= $ \sqrt {4(\sec^{2}\theta)}$
{ Writing $(\tan^{2}\theta + 1)$ as $ \sec^{2}\theta$ from second Pythagorean identity}
=$ \sqrt {4\sec^{2}\theta}$
= 2 $|\sec\theta|$
