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: 61


$2\sin 4x\cos x$

Work Step by Step

Use the first Sum-to-Product Formula, $\sin x+\sin y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}$. $\sin 5x+\sin 3x$ $=2\sin\frac{5x+3x}{2}\cos\frac{5x-3x}{2}$ $=2\sin\frac{8x}{2}\cos\frac{2x}{2}$ $=2\sin 4x\cos x$
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