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3.Trigonometrical Ratios, Functions and Identities
easy
$\sin 12^\circ \sin 48^\circ \sin 54^\circ = $
A
$1/16$
B
$1/32$
C
$1/8$
D
$1/4$
(IIT-1982)
Solution
(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}$.
Standard 11
Mathematics
