The value of sin 12 ° sin 48 ° sin 54 ° is equal to

Question

The value of $\sin 12 ° \sin 48 ° \sin 54 °$ is equal to

Smart Achievers · Accepted Answer

(3)

Now, $\sin 12 ° \sin 48 ° \sin 54 ° = \frac{1}{2} (\cos 36 ° - \cos 60 °) \cos 36 °$

$= \frac{1}{2} [\frac{\sqrt{5} + 1}{4} - \frac{1}{2}] [\frac{\sqrt{5} + 1}{4}]$

$= \frac{1}{2} [\frac{\sqrt{5} - 1}{4}] [\frac{\sqrt{5} + 1}{4}]$

$= \frac{5 - 1}{32} = \frac{4}{32} = \frac{1}{8}$

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