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: 40

Answer

$\displaystyle \frac{5}{2}\cos 5x+\frac{5}{2}\cos x$

Work Step by Step

Product-to-Sum: $\cos A \displaystyle \cos B=\frac{1}{2}[\cos(A+B)+\cos(A-B)]$ --------- $ 5\cos 3x \cos 2x=$ $=\displaystyle \frac{5}{2}[\cos(3x+2x)+\cos(3x-2x)]$ $=\displaystyle \frac{5}{2}[\cos 5x+\cos x]$ $=\displaystyle \frac{5}{2}\cos 5x+\frac{5}{2}\cos x$
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