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If 3tan^(-1)x +cot^(-1)x=pi, then x equa...

If `3tan^(-1)x +cot^(-1)x=pi`, then x equals to

A

0

B

1

C

`-1`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that `3tan^(-1)x + cot^(-1)x = pi"......"(i)`
`rArr 2tan^(-1)x+tan^(-1)x+cot^(-1)x = pi`
`rArr 2tan^(-1)x = pi - (pi)/(2), [:' tan^(-1)x + cot^(-1)x = pi/2]`
`rArr 2tan^(-1)x = (pi)/(2)`
`rArr tan^(-1)'(2x)/(1-x^(2)) = (pi)/(2), [:'2tan^(-1)x = tan^(-1)'(2x)/(1-x^(2)), AAx in (-1,1)]`
`rArr (2x)/(1-x^(2)) = tan'(pi)/(2)`
`rArr (2x)/(1-x^(2)) = 1/0 rArr 1 - x^(2) = 0`
`rArr x^(2) = 1 rArr x = +- 1 rArr x = 1`
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