Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 4 - Section 4.1 - Basic Graphs - 4.1 Problem Set - Page 192: 52

Answer

$\cos(-\theta)\tan(\theta)=\sin(\theta)$

Work Step by Step

$\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$ Since cosine is an even function, $\cos(-\theta)=\cos(\theta)$. These can be substituted back into the original equation: $\cos(-\theta)\tan(\theta)=\cos(\theta)\frac{\sin(\theta)}{\cos(\theta)}=\sin(\theta)$ Therefore the identity is true.
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