Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - Review Exercises - Page 552: 15



Work Step by Step

$cot^2θ+1=csc^2θ$ $csc^2 θ-1=cot^2θ$ $\frac{1}{cot^2 θ}=tan~θ$ $\frac{1}{csc~θ+1}-\frac{1}{csc~θ-1}=\frac{1}{csc~θ+1}\frac{csc~θ-1}{csc~θ-1}-\frac{1}{csc~θ-1}\frac{csc~θ+1}{csc~θ+1}=\frac{csc~θ-1}{csc^2~θ-1}-\frac{csc~θ+1}{csc^2~θ-1}=\frac{-2}{csc^2~θ-1}=-\frac{2}{cot^2θ}=2~tan^2~θ$
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