# 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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