Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 694: 87


$\sin 4x=4\sin x\cos x\cos 2x$

Work Step by Step

Start with the left side: $\sin 4x$ Rewrite $\sin 4x$ as $\sin (2*2x)$ and use the double-angle identity: $=\sin (2*2x)$ $=2\sin 2x\cos 2x$ Use the double-angle identity again: $=2(2\sin x\cos x)\cos 2x$ $=4\sin x\cos x\cos 2x$
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