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, $sin20^{\circ }sin40^{\circ }sin80^{\circ }$
$=sin20^{\circ }sin\left(60^{\circ }-20^{\circ }\right)sin\left(60^{\circ }+20^{\circ }\right)$
$=\frac{1}{4}sin3\left(20^{\circ }\right)=\frac{sin60^{\circ }}{4}=\frac{\sqrt{3}}{8}$