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 - Page 696: 25


$\dfrac {\cos ^{4}x-\sin ^{4}x}{\cos ^{2}x}=1-\tan ^{2}x$

Work Step by Step

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