Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.2 - Verifying Trigonometric Identities - 7.2 Exercises - Page 520: 30


The identity is verified. $\frac{sec~\theta-1}{1-cos~\theta}$: red $sec~\theta$: black

Work Step by Step

Remember: $sec~\theta=\frac{1}{cos~\theta}$ So: $sec~\theta~cos~\theta=\frac{1}{cos~\theta}~cos~\theta=1$ $\frac{sec~\theta-1}{1-cos~\theta}~\frac{1+cos~\theta}{1+cos~\theta}=\frac{sec~\theta+1-1-cos~\theta}{1-cos^2\theta}=\frac{sec~\theta-cos~\theta}{sin^2\theta}~\frac{cos~\theta}{cos~\theta}=\frac{1-cos^2\theta}{sin^2\theta~cos~\theta}=\frac{sin^2\theta}{sin^2\theta~cos~\theta}=\frac{1}{cos~\theta}=sec~\theta$
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.