Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - Summary Exercises Verifying Trigonometric Identities - Exercises: 14

Answer

$csc^{4}x-\cot ^{4}x=\dfrac {1+\cos ^{2}x}{1-\cos ^{2}x} $

Work Step by Step

$csc^{4}x-\cot ^{4}x=\dfrac {1}{\sin ^{4}x}-\dfrac {\cos ^{4}x}{\sin ^{4}x}=\dfrac {1-\left( \cos ^{2}x\right) ^{2}}{\sin ^{4}x}=\dfrac {\left( 1-\cos ^{2}x\right) \left( 1+\cos ^{2}x\right) }{\sin ^{4}x}=\dfrac {\sin ^{2}x\left( 1+\cos ^{2}x\right) }{\sin ^{4}x}=\dfrac {1+\cos ^{2}x}{\sin ^{2}x}=\dfrac {1+\cos ^{2}x}{1-\cos ^{2}x} $
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