Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

We know that $\sin \theta \sin \left(60-\theta \right)\sin \left(60+\theta \right)=\frac{1}{4}\sin 3\theta$

Now given $16\sin 20°\sin 40°\sin 80°$

Comparing with above formula $\theta =20°$

we get $16\sin 20°\sin 40°\sin 80°=16\times \frac{{\displaystyle 1}}{{\displaystyle 4}}\times \sin \left(3\times 20°\right)$

$=16\times \frac{1}{4}\times \sin 60°$ $=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}$