$sin 12^{\circ} sin 48^{\circ} sin 54^{\circ} =$

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Solution

The correct option is D 1/8
Given

$sin 12 sin 48 sin 54$

Multiplying and Dividing by $2$

$\frac{1}{2} (2 sin 12 sin 48) sin 54$

$(cos (A - B) - cos (A + B) = 2 sin A sin B)$

$\frac{1}{2} (cos 36 - cos 60) sin 54$

$\frac{1}{2} (cos 36 sin 54) - \frac{1}{2} (\frac{1}{2} sin 54)$

Multiplying and Dividing by $2$

$\frac{1}{4} ((2 cos 36 sin 54) - sin 54)$

$(sin (A + B) - sin (A - B) = 2 cos A sin B)$

$\frac{1}{4} (sin 90 - sin (- 18) - sin 54)$

$\frac{1}{4} (1 + \frac{\sqrt{5} - 1}{4} - \frac{\sqrt{5} + 1}{4})$

$\frac{1}{4} (\frac{4 + \sqrt{5} - 1 - \sqrt{5} - 1}{4})$

$\frac{1}{4} (\frac{2}{4})$

$\frac{1}{8}$

Suggest Corrections

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