$sin 12^{o} sin 48^{o} sin 54^{o} =$

\frac{1}{2}

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\frac{1}{4}

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\frac{1}{8}

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\frac{1}{16}

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Solution

The correct option is C $\frac{1}{8}$
$sin 12^{o} sin 48^{o} sin 54^{o} = \frac{1}{2} {sin 12^{o} sin 48^{o}} sin 54^{o}$
$= \frac{1}{2} {cos 36^{o} - cos 60^{o}} sin 54^{o} = \frac{1}{2} {cos 36^{o} sin 54^{o} - \frac{1}{2} sin 54^{o}}$
$= \frac{1}{4} {2 cos 36^{o} sin 54^{o} - sin 54^{o}} = \frac{1}{4} {sin 90^{o} + sin 18^{o} - sin 54^{o}}$
$= \frac{1}{4} {1 + \frac{\sqrt{5} - 1}{4} - \frac{\sqrt{5} + 1}{4}} = \frac{1}{4} \times \frac{1}{4} {4 + \sqrt{5} - 1 - \sqrt{5} - 1} = \frac{1}{8}$

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Similar questions

2^{1 / 4} {.4}^{1 / 8} {.8}^{1 / 16} {.16}^{1 / 32}

2^{1 / 4} \cdot 4^{1 / 8} . 8^{1 / 16} . 16^{1 / 32} . . . .

(2)^{\frac{1}{4}} . (4)^{\frac{1}{8}} . (8)^{\frac{1}{16}} . (16)^{\frac{1}{32}}

\frac{1}{2^{4}}, \frac{1}{4^{8}}, \frac{1}{8^{16}}, \frac{1}{16^{32}}

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