Question

Find the minimum value of n for which ${\tan }^{-1}\frac{n}{\pi }>\frac{\pi }{4},n\in N$.

Answer 1

${\tan }^{-1}\frac{n}{\pi }>\frac{\pi }{4}$

${\tan }^{-1}\frac{n}{\pi }>{\tan }^{-1}1$

$\tan \left({\tan }^{-1}\frac{n}{\pi }\right)>\tan \left({\tan }^{-1}1\right)$

$\frac{n}{\pi }>1$

$n>\pi$

$n>4,5,6,...$

Hence, the minimum value of n is 4.