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 667: 68


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

Work Step by Step

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