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: 45

Answer

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

Work Step by Step

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