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3.Trigonometrical Ratios, Functions and Identities
hard
The value of $sin\,10^o$ $sin\,30^o$ $sin\,50^o$ $sin\,70^o$ is
A
$\frac{1}{{36}}$
B
$\frac{1}{{32}}$
C
$\frac{1}{{18}}$
D
$\frac{1}{{16}}$
(JEE MAIN-2019)
Solution
$\sin \,{10^o}\,\sin \,{30^o}\,\sin \,{50^o}\,\sin \,{70^o}$
$ = \,\,\sin \,{10^o}\,\sin \,{30^o}\,\sin \,{50^o}\,\sin \,{70^o}$
$ = \,\,\sin \,{30^o}\,\{ \sin \,{10^o}\sin \,({60^o} – {10^o})\,\sin ({60^o} + {10^o})\,\} $
$ = \,\,\sin \,{30^o}\,\left\{ {\frac{1}{4}\sin \,3({{10}^o})} \right\}$
$ = \,\frac{1}{2}\left( {\frac{1}{4} \times \frac{1}{2}} \right)$
$ = \,\frac{1}{{16}}$
Standard 11
Mathematics
