\[\cos{110{^\circ}} + \cos{50{^\circ}} =\]
\[= 2\cos\frac{160{^\circ}}{2} \cdot \cos\frac{60{^\circ}}{2} =\]
\[= 2\cos{80{^\circ}} \cdot \cos{30{^\circ}} =\]
\[= 2\cos{80{^\circ}} \cdot \frac{\sqrt{3}}{2} = \sqrt{3}\cos{80{^\circ}}\]