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The number of solutions of the equation ...

The number of solutions of the equation `tan^(-1)(1+x)+tan^(-1)(1-x)=pi/2` is 2 (b) 3 (c) 1 (d) 0

A

2

B

3

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`tan^(-1) (1 + x) + tan^(-1) (1- x) = (pi)/(2)`
or `tan^(-1) (1 + x) = (pi)/(2) - tan^(-1) (1 -x)`
`= cot^(-1) (1 -x)`
`= tan^(-1) ((1)/(1 -x))`
or `1 + x = (1)/(1 -x)`
or `1 - x^(2) = 1`
or `x = 0`
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