Answer
$\csc^2\alpha$
Work Step by Step
$\frac{1}{\tan^2\alpha}+\cot\alpha\tan\alpha$
$=(\frac{1}{\tan\alpha})^2+\frac{\cos\alpha}{\sin\alpha}*\frac{\sin\alpha}{\cos\alpha}$
$=\cot^2\alpha+1$
$=\csc^2\alpha$
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 666: 42
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