Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - Summary Exercises Verifying Trigonometric Identities - Exercises: 9

Answer

$\cot \theta -\tan \theta =\dfrac {2\cos ^{2}\theta -1}{\sin \theta \cos \theta }$

Work Step by Step

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