Question

If $cot^{- 1}\frac{n}{\pi }>\frac{\pi }{6},n\in N,$ then the maximum value of $n$ is

Answer 1

$cot^{- 1}\frac{n}{\pi }>\frac{\pi }{6}$
$\Rightarrow \frac{n}{\pi } < cot\frac{\pi }{6}$
[as $cot^{- 1}x$ is a decreasing function ]
$\Rightarrow \frac{n}{\pi } < \sqrt{3}$
$\Rightarrow n < \sqrt{3}\pi $
$\Rightarrow n < 5.46$
$\Rightarrow $ maximum value of $n$ is $5$