Question

prove that ; $\sin {20}^{\circ }\sin {40}^{\circ }\sin {60}^{\circ }\sin {80}^{\circ }=\frac{3}{16}$

Answer 1

Implies that, $\sin 20.\sin 40.\sin 60.\sin 80$

$\frac{\sqrt{3}}{2}\left[\sin 20.\sin \left(60-20\right).\sin \left(60+20\right)\right]$

Implies that, $\frac{\sqrt{3}}{2}2\left[\sin 3\left(20\right)/4\right]$

Implies that, $\frac{\sqrt{3}}{2}2\left[\sin 60/4\right]$

Implies that, $\frac{\sqrt{3}}{2}\left[\sqrt{(}3/2)\times 4\right]$

Implies that, $\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{8}$

Implies that, $=\frac{3}{16}$