Aptitude Question ID : 94449

The value of \cot 10^{\circ}\cdot \cot 20^{\circ}\cdot \cot 60^{\circ}\cdot \cot 70^{\circ}\cdot \cot 80^{\circ} is :
[A]-1
[B]1
[C]\frac{1}{\sqrt{3}}
[D]\sqrt{3}

\mathbf{\frac{1}{\sqrt{3}}}
\cot 10^{\circ}\cdot \cot 80^{\circ}\cdot \cot 20^{\circ}\cdot \cot 70^{\circ}\cdot \cot 60^{\circ}
= \cot 10^{\circ}\cdot \tan 10^{\circ}\cdot \cot 20^{\circ}\cdot \tan 20^{\circ}\cdot \cot 60^{\circ}
\left [ \because \tan\left ( 90^{\circ}- \Theta \right )  = \cot \Theta \right ]
\left [ \tan\Theta \cdot \cot \Theta = 1 \right ]
= 1\times 1\times \frac{1}{\sqrt{3}} \left [ \because \cot 60^{\circ} = \frac{1}{\sqrt{3}} \right ]
= \frac{1}{\sqrt{3}}
Hence option [C] is correct answer.

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