\[\cos{70{^\circ}} + \cos{50{^\circ}} =\]
\[= 2\cos\frac{120{^\circ}}{2} \cdot \cos\frac{20{^\circ}}{2} =\]
\[= 2\cos{60{^\circ}} \cdot \cos{10{^\circ}} =\]
\[= 2 \cdot \frac{1}{2} \cdot \cos{10{^\circ}} = \cos{10{^\circ}}\]