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: 60

Answer

$2\tan \theta $

Work Step by Step

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