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 - Page 659: 69


$\cot \theta -\tan \theta $

Work Step by Step

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