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 - Page 696: 21


$\dfrac {\cot s-\tan s}{\cos s+\sin s}=\dfrac {\cos s-\sin s}{\cos s\sin s}$

Work Step by Step

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