The value of $sin 20^{o} . sin 40^{o} . sin 80^{o}$ is

\frac{\sqrt{3}}{8}

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\frac{1}{8}

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\frac{1}{16}

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N o n e o f t h e s e

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Solution

The correct option is A $\frac{\sqrt{3}}{8}$
$sin 20^{o} sin 40^{o} sin 80^{o}$
$\to$ we know that,
$sin A sin (60 - A) sin (60 + A) = \frac{1}{4} sin 3 A$
$∴ sin 20^{o} sin 40^{o} sin 80^{o} = \frac{1}{4} \times sin (20 \times 3)$
$∴ sin 20^{o} sin 40^{o} sin 80^{o} = (\frac{\sqrt{3}}{8})$

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