Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.4 Trigonometric Identities - 7.4 Assess Your Understanding - Page 476: 46

Answer

See explanations.

Work Step by Step

Multiply the left side numerator and the denominator by $sin(v)$ and use the relation $csc(v)=\frac{1}{sin(v)}$. We have $LHS=\frac{sin(v)csc(v)-sin(v)}{sin(v)csc(v)+sin(v)}=\frac{1-sin(v)}{1+sin(v)}=RHS$
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