Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.1 - Verifying Trigonometric Identities - Exercise Set - Page 658: 20


See the explanation below.

Work Step by Step

$\frac{{{\sec }^{2}}t}{\tan t}=\sec t\csc t$ Recall Trigonometric Identities, $\begin{align} & \csc t=\frac{1}{\sin t} \\ & \sec t=\frac{1}{\cos t} \\ & \tan t=\frac{\sin t}{\cos t} \\ \end{align}$ Use the above identities and solve the left side of the given expression, $\begin{align} & \frac{{{\sec }^{2}}t}{\tan t}=\frac{1}{{{\cos }^{2}}t}\left( \frac{\cos t}{\sin t} \right) \\ & =\frac{1}{\cos t}\left( \frac{1}{\sin t} \right) \\ & =\sec t\csc t \end{align}$ Therefore, $\frac{{{\sec }^{2}}t}{\tan t}=\sec t\csc t$
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