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The minimum value of n for which tan^(-1...

The minimum value of n for which `tan^(-1)'n/pi gt (pi)/(4), n in N`, is valid is 5.

A

2

B

4

C

6

D

1

Text Solution

Verified by Experts

We have
`tan^(-1)(n)/(pi)gt(pi)/(4)`
`rarr tan^(-1)(n)/(pi)gttan^(-1)1`
`rarr tan(tan^(-1)(n)/(pi))gttan(tan^(-1)1)` [before `tan theta` is an increasing function ]
`rarr (n)/(pi)ge1`
`rarr ngtpi=3.14` ltbvrgt `rarr n=4,5,6…`
Hence the minimum value of n is 4
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