Question

Value of $\sin 12^{\circ}.\sin \, 48^{\circ}.\sin \, 54^{\circ} $ is:

• A. $\frac{-1}{8}$
• B. 8
• C. $\frac{1}{8}$
• D. - 8

Answer 1

Answer: (C)

Let $\theta = 12^{\circ}$
Consider given expression
$= \frac{1}{\sin 72^{\circ}} \sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ} \sin 72^{\circ}$
$ = \frac{1}{2} \frac{\sin 3(12^{\circ}) \sin 54^{\circ}}{\sin 72^{\circ}}$
$ = \frac{\sin36^{\circ} \sin54^{\circ}}{8\sin36^{\circ} \cos36^{\circ}}$
$ = \frac{\cos36^{\circ}}{8 \cos36^{\circ}} $
$= \frac{1}{8}$