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: 71


$\sin ^{2}\alpha sec^2\alpha +\sin ^{2}\alpha csc^2\alpha =sec^2\alpha $

Work Step by Step

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