Answer
The given statement makes sense.
Work Step by Step
One of the sum-to-product formulas is $\cos \alpha +\cos \beta =2\cos \frac{\alpha +\beta }{2}\cos \frac{\alpha -\beta }{2}$. So in this question, according to the above-mentioned formula, the value of $\alpha $ is ${{47}^{\circ }}$ and the value of $\beta $ is ${{59}^{\circ }}$.
Now, the expression can be evaluated as provided below:
$\begin{align}
& \cos {{47}^{\circ }}+\cos {{59}^{\circ }}=2\cos \left( \frac{{{47}^{\circ }}+{{59}^{\circ }}}{2} \right)\cos \left( \frac{{{47}^{\circ }}-{{59}^{\circ }}}{2} \right) \\
& =2\cos \left( \frac{{{106}^{\circ }}}{2} \right)\cos \left( \frac{-{{12}^{\circ }}}{2} \right) \\
& =2\cos {{53}^{\circ }}\cos \left( -{{6}^{\circ }} \right)
\end{align}$
Now, applying the even-odd identity, which is $cos(-x)=\cos x$, the expression can be further evaluated as given below:
$2\cos {{53}^{\circ }}\cos \left( -{{6}^{\circ }} \right)=2\cos {{53}^{\circ }}\cos {{6}^{\circ }}$
Thus, $cos{{47}^{\circ }}+cos{{59}^{\circ }}$ can be expressed as $2\cos {{53}^{\circ }}\cos {{6}^{\circ }}$.
