यदि x = cos 10^circ cos 20^circ cos 40^circ | vedclass

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Question

$x = \cos \,\,{10^o}\,\cos \,\,{20^o}\,\,\cos \,\,{40^o}$

$ = \frac{1}{{2\,\,\sin \,\,{{10}^o}}}\,[2\,\,\sin \,\,{10^o}\cos \,\,{10^o}\cos \,\,{20^

Vedclass · Accepted Answer

$\frac{1}{8}\cot 10^\circ $

Vedclass · Answer

$x = \cos \,\,{10^o}\,\cos \,\,{20^o}\,\,\cos \,\,{40^o}$

$ = \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}$.

यदि $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ $ हो, तो $x$ का मान होगा

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