- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
જો $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ ,$ તો $x =.....$
A
$\frac{1}{4}\tan 10^\circ $
B
$\frac{1}{8}\cot 10^\circ $
C
$\frac{1}{8}{\rm{cosec}}10^\circ $
D
$\frac{1}{8}\sec 10^\circ $
Solution
(b) $x = \cos \,\,{10^o}\,\cos \,\,{20^o}\,\,\cos \,\,{40^o}$
$ = \frac{1}{{2\,\,\sin \,\,{{10}^o}}}\,[2\,\,\sin \,\,{10^o}\cos \,\,{10^o}\cos \,\,{20^o}\,\,\cos \,\,{40^o}]$
$ = \frac{1}{{2\,.\,2\,\,\sin \,\,{{10}^o}}}\,[2\,\,\sin \,\,{20^o}\cos \,\,{20^o}\,\,\cos \,\,{40^o}]$
$ = \frac{1}{{2\,.\,4\sin {{10}^o}}}[2\sin {40^o}\cos {40^o}) = \frac{1}{{8\sin {{10}^o}}}(\sin {80^o})$
$ = \frac{1}{{8\,\,\sin \,\,{{10}^o}}}\cos \,\,{10^o} = \frac{1}{8}\cot \,\,{10^o}$.
Standard 11
Mathematics
