\[\cos{47{^\circ}} \cdot \cos{2{^\circ}} =\]
\[= \frac{1}{2} \cdot \left( \cos{49{^\circ}} + \cos{45{^\circ}} \right) =\]
\[= \frac{1}{2} \cdot \left( \cos{49{^\circ}} + \frac{\sqrt{2}}{2} \right) =\]
\[= \frac{1}{2}\cos{49{^\circ}} + \frac{\sqrt{2}}{4}\]