Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.3 Sum and Difference Identities - 7.3 Exercises - Page 680: 94


$\sin(x+y)+\sin(x-y)=2\sin x\cos y$

Work Step by Step

Start with the left side: $\sin(x+y)+\sin(x-y)$ Use the sum and difference formulas on page 673: $=(\sin x\cos y+\cos x\sin y)+(\sin x\cos y-\cos x\sin y)$ $=\sin x\cos y+\cos x\sin y+\sin x\cos y-\cos x\sin y$ $=2\sin x\cos y$ Since this equals the right side, the identity has been proven.
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