## Trigonometry 7th Edition

2 $|\sec\theta|$
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 $|\sec\theta|$