The value of $sin 20 ° sin 40 ° sin 80 °$ equals

\frac{\sqrt{3}}{2}

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\frac{\sqrt{3}}{4}

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

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\frac{1}{8}

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Solution

The correct option is C $\frac{\sqrt{3}}{8}$
Let ,
$X = sin 20 ° sin 40 ° sin 80 ° \Rightarrow X = \frac{sin 20 °}{2} (cos 40 ° - cos 120 °) \Rightarrow X = \frac{1}{4} (sin 60 ° - sin 20 °) + \frac{1}{4} sin 20 ° \Rightarrow X = \frac{sin 60 °}{4} = \frac{\sqrt{3}}{8}$

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Similar questions

sin 10^{\circ} + sin 20^{\circ} + sin 40^{\circ} + sin 50^{\circ} = sin 70^{\circ} + sin 80^{\circ}

Sin40/sin80 + sin80/sin20 - sin20/sin40

A 1

B 2

C 3

D 4

sin 20^{0} sin 40^{0} sin 80^{0}

$s i n 20^{\circ} s i n 40^{\circ} s i n 60^{\circ} s i n 80^{\circ}$ =

sin 20^{\circ} sin 40^{\circ} sin 60^{\circ} sin 80^{\circ} = \frac{k}{16}

k

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