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)

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