\[\cos{37{^\circ}} \cdot \cos{23{^\circ}} =\]
\[= \frac{1}{2} \cdot \left( \cos{60{^\circ}} + \cos{14{^\circ}} \right) =\]
\[= \frac{1}{2} \cdot \left( \frac{1}{2} + \cos{14{^\circ}} \right) =\]
\[= \frac{1}{4} + \frac{1}{2}\cos{14{^\circ}}\]