# 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.