Precalculus (6th Edition) Blitzer

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

Chapter 5 - Section 5.2 - Sum and Difference Formulas - Exercise Set - Page 670: 75


The right-hand side is equal to $\cos 3x$.

Work Step by Step

By using the identity $\cos \left( \alpha -\beta \right)=\cos \alpha \cos \beta +\sin \alpha \sin \beta $ , the above expression can be simplified as: $\begin{align} & \cos \ 2x\ \cos \ 5x\ +\sin \ 2x\ 5x=\cos \left( 2x-5x \right) \\ & =\cos \left( -3x \right) \\ & =\cos 3x \end{align}$ Thus, the right side of the equation is equal to $\cos 3x$. Thus, it is proved that left side is equal to the right side.
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