## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 5 - Review Exercises - Page 707: 18

#### Answer

The required solution is $\frac{1}{2}$

#### Work Step by Step

We use the difference formula $\cos \left( x-y \right)$: $\cos \left( x-y \right)=\cos x\operatorname{cosy}+\sin x\sin y$ Then, using the above formula, compute the value of $\cos {{65}^{\circ }}\cos {{5}^{\circ }}+\sin {{65}^{\circ }}\sin {{5}^{\circ }}$. \begin{align} & \cos {{65}^{\circ }}\cos {{5}^{\circ }}+\sin {{65}^{\circ }}\sin {{5}^{\circ }}=\cos \left( {{65}^{\circ }}-{{5}^{\circ }} \right) \\ & =\cos {{60}^{\circ }} \\ & =\frac{1}{2} \end{align}

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