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: 65

Answer

$-2\cos\frac{9x}{2}\sin\frac{5x}{2}$

Work Step by Step

Use the second Sum-to-Product Formula, $\sin x-\sin y=2\cos\frac{x+y}{2}\sin\frac{x-y}{2}$. $\sin 2x-\sin 7x$ $=2\cos\frac{2x+7x}{2}\sin\frac{2-7x}{2}$ $=2\cos\frac{9x}{2}\sin\frac{-5x}{2}$ $=-2\cos\frac{9x}{2}\sin\frac{5x}{2}$
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