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 $\cos {{65}^{\circ }}\cos {{5}^{\circ }}+\sin {{65}^{\circ }}\sin {{5}^{\circ }}$.
$\begin{align}
& \cos {{65}^{\circ }}\cos {{5}^{\circ }}+\sin {{65}^{\circ }}\sin {{5}^{\circ }}=\cos \left( {{65}^{\circ }}-{{5}^{\circ }} \right) \\
& =\cos {{60}^{\circ }} \\
& =\frac{1}{2}
\end{align}$
