The value of sin 10-sin 30-sin 50-sin 70- is -

Sin 10^∘sin 30^∘sin 50^∘sin 70^∘ =14sin 10^∘(2sin 50^∘sin 70^∘) =14sin 10^∘(cos 20^∘ cos 120^∘) =18(2sin 10^∘cos 20^∘)+18sin 10^∘ =18sin 30^∘ 18sin 10^∘+18sin 1 ...

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Byju's Answer

Standard XIII

Mathematics

Product of Trigonometric Ratios in Terms of Their Sum

The value of ...

Question

The value of $sin 10^{\circ} sin 30^{\circ} sin 50^{\circ} sin 70^{\circ}$ is :

\frac{1}{32}

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\frac{1}{16}

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\frac{1}{18}

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\frac{1}{36}

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Solution

The correct option is B $\frac{1}{16}$
$sin 10^{\circ} sin 30^{\circ} sin 50^{\circ} sin 70^{\circ}$
$= \frac{1}{4} sin 10^{\circ} (2 sin 50^{\circ} sin 70^{\circ})$
$= \frac{1}{4} sin 10^{\circ} (cos 20^{\circ} - cos 120^{\circ})$
$= \frac{1}{8} (2 sin 10^{\circ} cos 20^{\circ}) + \frac{1}{8} sin 10^{\circ}$
$= \frac{1}{8} sin 30^{\circ} - \frac{1}{8} sin 10^{\circ} + \frac{1}{8} sin 10^{\circ}$
$= \frac{1}{16}$

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The value of sin10∘sin30∘sin50∘sin70∘ is :

The correct option is B 116sin10∘sin30∘sin50∘sin70∘ =14sin10∘(2sin50∘sin70∘) =14sin10∘(cos20∘−cos120∘) =18(2sin10∘cos20∘)+18sin10∘ =18sin30∘−18sin10∘+18sin10∘ =116

The value of $sin 10^{\circ} sin 30^{\circ} sin 50^{\circ} sin 70^{\circ}$ is :