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: 22

Answer

Proven below.

Work Step by Step

The identity says: $tan(\theta)=\frac{sin\theta}{cos\theta}$ and $sec(\theta)=\frac{1}{cos(\theta)}$. Hence $sin(\theta)\cdot sec(\theta)=sin(\theta)\cdot \frac{1}{cos(\theta)}=\frac{sin(\theta)}{cos(\theta)}=tan\theta.$
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