Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.1 Fundamental Identities - 7.1 Exercises: 70

Answer

$\tan \theta -\cot \theta $

Work Step by Step

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