Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 63


$2\sin 5x\sin x$

Work Step by Step

Use the second Sum-to-Product Formula, $\cos x-\cos y=-2\sin\frac{x+y}{2}\sin\frac{x-y}{2}$. $\cos 4x-\cos 6x$ $=-2\sin\frac{4x+6x}{2}\sin\frac{4x-6x}{2}$ $=-2\sin\frac{10x}{2}\sin\frac{-2x}{2}$ $=-2\sin 5x \sin(-x)$ $=2\sin 5x\sin x$
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