Explanation

(c)
Now,$\ \sin{12{^\circ}\sin{48{^\circ}\sin{54{^\circ}}}}$
$= \frac{1}{2}(\cos{36{^\circ} - \cos{60{^\circ})\cos{36{^\circ}}}}$
$= \frac{1}{2}\left\lbrack \frac{\sqrt{5} + 1}{4} - \frac{1}{2} \right\rbrack\left\lbrack \frac{\sqrt{5} + 1}{4} \right\rbrack$
$= \frac{1}{2}\left\lbrack \frac{\sqrt{5} - 1}{4} \right\rbrack\left\lbrack \frac{\sqrt{5} + 1}{4} \right\rbrack$
$= \frac{5 - 1}{32} = \frac{4}{32} = \frac{1}{8}$