Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.5 Double-Angle Identities - 5.5 Exercises - Page 237: 60


$$5\cos3x\cos2x=\frac{5}{2}(\cos 5x+\cos x)$$

Work Step by Step

$$A=5\cos3x\cos2x$$ The product-to-sum identity that will be applied here is $$\cos X\cos Y=\frac{1}{2}[\cos(X+Y)+\cos(X-Y)]$$ Therefore, A would be $$A=5\times\frac{1}{2}[\cos(3x+2x)+\cos(3x-2x)]$$ $$A=\frac{5}{2}(\cos 5x+\cos x)$$
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