Answer
See below.
Work Step by Step
$LHS=csc\theta-sin\theta
=\frac{1}{sin\theta}-sin\theta
=\frac{1-sin^2\theta}{sin\theta}
=\frac{cos^2\theta}{sin\theta}
=cos\theta cot\theta
=RHS$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Chapter Review - Review Exercises - Page 527: 34
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