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: 64

Answer

10 $|\sec\theta|$

Work Step by Step

Given expression- $ \sqrt {4x^{2} + 100}$ Substituting $5\tan\theta$ for $x$ as given, the expression becomes- $ \sqrt {4(5\tan\theta)^{2} + 100}$ = $ \sqrt {4(25\tan^{2}\theta) + 100}$ = $ \sqrt {100\tan^{2}\theta + 100}$ = $ \sqrt {100(\tan^{2}\theta + 1)}$ = $ \sqrt {100 \sec^{2}\theta}$ { Writing $(\tan^{2}\theta + 1)$ as $ \sec^{2}\theta$ from second Pythagorean identity} = 10 $|\sec\theta|$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.