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: 61

Answer

$\dfrac {1}{1-\sin \theta }+\dfrac {1}{1+\sin \theta }=2sec^{2}\theta $

Work Step by Step

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