Question

$\sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}$ is equal to :

• A. 1/16
• B. 1/32
• C. 1/8
• D. 1/4

Answer 1

Answer: (C)

$\sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}$
$=\frac{1}{2}\left[2 \sin 12^{\circ} \sin 48^{\circ}\right] \sin \left(90^{\circ}-36^{\circ}\right)$
$=\frac{1}{2}\left[\cos 36^{\circ}-\cos 60^{\circ}\right] \cos 36^{\circ}$
$=\frac{1}{2}\left[\frac{\sqrt{5}+1}{4}-\frac{1}{2}\right]\left(\frac{\sqrt{5}+1}{4}\right)$
$=\frac{1}{32}[5+1+2 \sqrt{5}-2(\sqrt{5}+1)]$
$=\frac{1}{32}[4]=\frac{1}{8}$