Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 666: 21


$-2\cos xcsc^{2}x$

Work Step by Step

$\dfrac {1}{1+\cos x}-\dfrac {1}{1-\cos x}=\dfrac {\left( 1-\cos x\right) -\left( 1+\cos x\right) }{\left( 1+\cos x\right) \left( 1-\cos x\right) }=\dfrac {-2\cos x}{1-\cos ^{2}x}=\dfrac {-2\cos x}{\sin ^{2}x}=-2\cos xcsc^{2}x$
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