12^ 48^ 54^ = - Vidyadip

MCQ

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

A
$1/16$
B
$1/32$
✓
$1/8$
D
$1/4$

✓

Answer

Correct option: C.

$1/8$

c
(c) $\sin \,{12^o}\,\sin \,{48^o}\,\sin \,{54^o} = \frac{1}{2}\,\left\{ {\cos {{36}^o} - \cos {{60}^o}} \right\}\,\cos \,{36^o}$

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

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

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

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