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)

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