\[\sin{36{^\circ}} \cdot \sin{24{^\circ}} =\]
\[= \frac{1}{2} \cdot \left( \cos{12{^\circ}} - \cos{60{^\circ}} \right) =\]
\[= \frac{1}{2} \cdot \left( \cos{12{^\circ}} - \frac{1}{2} \right) =\]
\[= \frac{1}{2}\cos{12{^\circ}} - \frac{1}{4}\]