Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.5 - More on Identities - 1.5 Problem Set - Page 46: 58

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} = $|\sec\theta|$
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