Question

The value of $\sin 20°\sin 40°\sin 80°$ equals

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

Answer 1

The correct option is C $\frac{\sqrt{3}}{8}$

Let ,
$X=\sin 20°\sin 40°\sin 80°\Rightarrow X=\frac{\sin 20°}{2}(\cos 40°-\cos 120°)\Rightarrow X=\frac{1}{4}(\sin 60°-\sin 20°)+\frac{1}{4}\sin 20°\Rightarrow X=\frac{\sin 60°}{4}=\frac{\sqrt{3}}{8}$