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: 76

Answer

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

Work Step by Step

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