[16 (20^ ) (40^ ) (80^ )] is equal to :

Question

$$16\sin (20^\circ )\sin (40^\circ )\sin (80^\circ )$$ is equal to :

Accepted Answer

Using $\sin\theta\sin(60^\circ-\theta)\sin(60^\circ+\theta) = \dfrac14\sin3\theta$ with $\theta=20^\circ$:

$$\sin20^\circ\sin40^\circ\sin80^\circ = \sin20^\circ\sin(60^\circ-20^\circ)\sin(60^\circ+20^\circ) = \frac14\sin60^\circ = \frac{\sqrt3}8$$

$$16\times\frac{\sqrt3}8 = 2\sqrt3$$

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