Sin,10^o sin,30^o sin,50^o sin,70^o ની કિમત ....... થાય.

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3.Trigonometrical Ratios, Functions and Identities

hard

$sin\,10^o$ $sin\,30^o$ $sin\,50^o$ $sin\,70^o$ ની કિમત ....... થાય.

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

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