Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.4 - Product-to-Sum and Sum-to-Product Formulas - Exercise Set - Page 689: 3


The required solution is $\frac{1}{2}\left[ \cos 4x+\cos 10x \right]$.

Work Step by Step

One of the product-to-sum formulas is $\cos \alpha \cos \beta =\frac{1}{2}\left[ \cos \left( \alpha -\beta \right)+\cos \left( \alpha +\beta \right) \right]$. So, tn this question, according to the above-mentioned formula, the value of $\alpha $ is $7x$ and the value of $\beta $ is $3x$. Thus, the expression can be evaluated as provided below. $\begin{align} & \cos 7x\cos 3x=\frac{1}{2}\left[ \cos \left( 7x-3x \right)+\cos \left( 7x+3x \right) \right] \\ & =\frac{1}{2}\left[ \cos 4x+\cos 10x \right] \end{align}$
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