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: 81


$(\cos 2x+\sin 2x)^2=1+\sin 4x$

Work Step by Step

Start with the left side: $(\cos 2x+\sin 2x)^2$ Expand: $=\cos^2 2x+2\cos 2x\sin 2x+\sin^2 2x$ Rearrange terms: $=\cos^2 2x+\sin^2 2x+2\cos 2x\sin 2x$ Use the identities $\cos^2 \theta+\sin^2\theta=1$ and $2\cos\theta\sin\theta=\sin 2\theta$, where $\theta=2x$: $=1+\sin (2*2x)$ $=1+\sin 4x$
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