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: 53



Work Step by Step

$\sec(-\theta)$ can be written as $\frac{1}{\cos(-\theta)}$ $\cot(-\theta)$ can also be written as $\frac{\cos(-\theta)}{\sin(-\theta)}$. As such, $\sin(-\theta)\sec(-\theta)\cot(-\theta)=\sin(-\theta)\frac{1}{\cos(-\theta)}\frac{\cos(-\theta)}{\sin(-\theta)}=1$. The trigonometric terms in the equation cancel out, therefore, $\sin(-\theta)\sec(-\theta)\cot(-\theta)=1$.
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