Question

$16\sin \left(20^{\circ }\right)\sin \left(40^{\circ }\right)\sin \left(80^{\circ }\right)$ is equal to :

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

Answer 1

Answer: (B)

$16\sin 20^{\circ }\sin 40^{\circ }\sin 80^{\circ }$
$=16\sin 40^{\circ }\sin 20^{\circ }\sin 80^{\circ }$
$=4(4\sin (60-20)\sin (20)\sin (60+20))$
$=4\times \sin \left(3\times 20^{\circ }\right)$
$[\because \sin 3\theta =4\sin (60-\theta )\times \sin \theta \times \sin (60+\theta )]$
$=4\times \sin 60^{\circ }$
$=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}$