Algebra and Trigonometry 10th Edition

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

Chapter 7 - Review Exercises - Page 553: 65


The identity is verified. $\frac{csc~θ}{2~cos~θ}=csc~2θ$

Work Step by Step

Use: $2~sin~θ~cos~θ=sin~2θ$ and $csc~θ=\frac{1}{sin~θ}$ Start on the right side: $\frac{csc~θ}{2~cos~θ}=csc~θ~\frac{1}{2~cos~θ}=\frac{1}{sin~θ}~\frac{1}{2~cos~θ}=\frac{1}{2~sin~θ~cos~θ}=\frac{1}{sin~2θ}=csc~2θ$
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