A solution of the equation
`tan^(-1)(1+x)+tan^(-1)(1-x)=(pi)/(2)` is

Options

A. x = 1
B. x = -1
C. x = 0
D. `x = (1)/(2)`

Answer

C

Explanation

`tan^(-1)(1+x)+tan^(-1)(1-x)=(pi)/(2)`
`tan^(-1)[((1+x)+(1-x))/(1-(1+x)(1-x))]=(pi)/(2)`
`rArr (1+x+1-x)/(1-(1+x)(1-x))="tan"(pi)/(2)`
`rArr (2)/(1-(1+x)(1-x))=(1)/(0)`
`rArr 1 - (1+x) (1-x) = 0`
`rArr (1+x) (1-x) = 1`
`1 - x^(2) = 1`
`x^(2) = 0`
x = 0
`therefore` Option (c) is correct.