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: 59

Answer

$\frac{3}{2}(\cos 11x+\cos 3x)$

Work Step by Step

Use the third Sum-to-Product Formula on page 559, $\cos u\cos v=\frac{1}{2}[\cos(u+v)+\cos(u-v)]$. $3\cos 4x\cos 7x$ $=3\times\frac{1}{2}[\cos(4x+7x)+\cos(4x-7x)]$ $=\frac{3}{2}[(\cos 11x+\cos (-3x)]$ $=\frac{3}{2}(\cos 11x+\cos 3x)$
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