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
$=\frac{1}{\sin 72^{\circ }}\sin 12^{\circ }\sin 48^{\circ }\sin 54^{\circ }\sin 72^{\circ }$
$=\frac{1}{2}\frac{\sin 3(12^{\circ })\sin 54^{\circ }}{\sin 72^{\circ }}$
$=\frac{\sin 36^{\circ }\sin 54^{\circ }}{8\sin 36^{\circ }\cos 36^{\circ }}$
$=\frac{\cos 36^{\circ }}{8\cos 36^{\circ }}$
$=\frac{1}{8}$