Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - Chapter 7 Test Prep - Review Exercises: 57

Answer

$\tan \theta\sin 2\theta=2-2\cos^2 \theta$

Work Step by Step

Simplify the left side: $\tan \theta\sin 2\theta$ $=\frac{\sin\theta}{\cos\theta}*2\sin\theta\cos\theta$ $=2\sin^2\theta$ Simplify the right side: $2-2\cos^2 \theta$ $=2(1-\cos^2 \theta)$ $=2\sin^2\theta$ Since both the left side and the right side are equal to $2\sin^2\theta$, they are equal to each other, and the identity has been proven.
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