Question

The value of $\sin 20^{\circ} \; \sin 40^{\circ} \; \sin 80^{\circ} $ equals

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{3}}{4}$
• C. $\frac{\sqrt{3}}{8}$
• D. $\frac{1}{8}$

Answer 1

Answer: (C)

We have, $ sin \,20^{\circ} \,sin \,40^{\circ}\, sin\, 80^{\circ} $
$ = sin\, 20^{\circ}\, sin\left(60^{\circ} - 20^{\circ}\right) sin\left(60^{\circ}+20^{\circ}\right) $
$= \frac{1}{4} sin \,3 \left(20^{\circ}\right) = \frac{sin\, 60^{\circ}}{4} = \frac{\sqrt{3}}{8}$