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: 10


$\dfrac {1}{sect-1}+\dfrac {1}{sect+1}=\dfrac {2\cos t}{\sin ^{2}t}=2\cot t \csc t$

Work Step by Step

$\dfrac {1}{sect-1}+\dfrac {1}{sect+1}=\dfrac {2sect}{\left( sect-1\right) \left( sect+1\right) }=\dfrac {2sect}{sec^{2}t-1}=\dfrac {\dfrac {2}{\cos t}}{\dfrac {1}{\cos ^{2}t}-1}=\dfrac {2\cos t}{\sin ^{2}t}=2\cot t \csc t$
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