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: 79

Answer

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

Work Step by Step

Start with the left side: $(\sin x+\cos x)^2$ Expand: $=\sin^2 x+2\sin x\cos x+\cos^2 x$ Rearrange terms: $=2\sin x\cos x+(\sin^2 x+\cos^2 x)$ Use the identities $2\sin x\cos x=\sin 2x$ and $\sin^2 x+\cos^2 x=1$: $=\sin 2x+1$ Since this equals the right side, the identity has been proven.
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