Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.1 - Using Fundamental Identities - 7.1 Exercises - Page 513: 48

Answer

$\frac{cos~x}{1+sin~x}+\frac{1+sin~x}{cos~x}=2~sec~x$

Work Step by Step

$\frac{cos~x}{1+sin~x}+\frac{1+sin~x}{cos~x}=\frac{cos~x}{1+sin~x}\frac{cos~x}{cos~x}+\frac{1+sin~x}{cos~x}\frac{1+sin~x}{1+sin~x}=\frac{cos^2x+sin^2x+1+2~sin~x}{cos~x(1+sin~x)}=\frac{2(1+sin~x)}{cos~x(1+sin~x)}=\frac{2}{cos~x}=2~sec~x$
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.