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: 57


$\frac{1}{2}(\sin 5x+\sin 3x)$

Work Step by Step

Use the second Product-to-Sum Formula on page 559, $\cos u\sin v=\frac{1}{2}[\sin(u+v)-\sin(u-v)]$. $\cos x\sin 4x $ $=\frac{1}{2}[\sin(x+4x)-\sin(x-4x)]$ $=\frac{1}{2}[\sin(5x)-\sin(-3x)]$ $=\frac{1}{2}(\sin 5x+\sin 3x)$
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