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: 78

Answer

The right side is equal to $\cos \frac{x}{2}$.

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: $\begin{align} & \cos \frac{5x}{2}\cos 2x+\sin \frac{5x}{2}\sin 2x=\cos \left( \frac{5x}{2}-2x \right) \\ & =\cos \left( \frac{5x-4x}{2} \right) \\ & =\cos \frac{x}{2} \end{align}$ Thus, the right side of the equation is equal to $\cos \frac{x}{2}$. Thus, it is proved that left side is equal to the right side.
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