The value of $\sin {12}^{\circ }\sin {48}^{\circ }\sin {54}^{\circ }$ is equal to

Now,

$\begin{array}{l}\sin {12}^{\circ }\sin {48}^{\circ }\sin {54}^{\circ }\\ =\frac{1}{2}\left(\cos {36}^{\circ }-\cos {60}^{\circ }\right)\cos {36}^{\circ }\\ =\frac{1}{2}\left[\frac{\sqrt{5}+1}{4}-\frac{1}{2}\right]\left[\frac{\sqrt{5}+1}{4}\right]\\ =\frac{1}{2}\left[\frac{\sqrt{5}-1}{4}\right]\left[\frac{\sqrt{5}+1}{4}\right]\\ =\frac{5-1}{32}=\frac{4}{32}=\frac{1}{8}\end{array}$