Question

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

(A) 116

(B) 1/32

(C) $1 / 8$

(D) $1 / 4$

Answer 1

$\because \sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}$

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

So, The correct option will be (C).