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: 18


$\dfrac {\sin s}{1+\cos s}+\dfrac {1+\cos s}{\sin s}=\dfrac {2}{\sin s}=2cscs$

Work Step by Step

$\dfrac {\sin s}{1+\cos s}+\dfrac {1+\cos s}{\sin s}=\dfrac {\sin ^{2}s+\left( 1+\cos s\right) ^{2}}{\sin s\left( 1+\cos s\right) }=\dfrac {\sin ^{2}s+1+2\cos s+\cos ^{2}s}{\sin s\left( 1+\cos s\right) }=\dfrac {2\left( 1+\cos s\right) }{\sin s\left( 1+\cos s\right) }=\dfrac {2}{\sin s}=2cscs$
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