Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises: 31

Answer

$$\sec^{2}\theta$$

Work Step by Step

Simplify $$\tan\theta(\cot\theta+\tan\theta)$$ Use the Reciprocal Identity $$\cot\theta= \frac{1}{\tan\theta}$$ to obtain $$\tan\theta\bigg(\frac{1}{\tan\theta}+\tan\theta\bigg)=1+\tan^{2}\theta.$$ Finally, use the Pythagorean Identity $$1+\tan^{2}\theta=\sec^{2}\theta$$ to obtain $$\tan\theta(\cot\theta+\tan\theta)=\sec^{2}\theta.$$
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