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: 6


$\dfrac {1-\sin t}{\cos t}=\dfrac {1}{sect+\tan t}$

Work Step by Step

$\dfrac {1-\sin t}{\cos t}=\dfrac {\left( 1-\sin t\right) \left( 1+\sin t\right) }{\cos t\left( 1+\sin t\right) }=\dfrac {\cos ^{2}t}{\cos t\left( 1+\sin t\right) }=\dfrac {\cos t}{1+\sin t}=\dfrac {\cos t/\cos t}{\dfrac {1}{\cos t}+\dfrac {\sin t}{\cos t}}=\dfrac {1}{sect+\tan t}$
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