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