If `tan^(-1) ((x+1)/(x-1))+tan^(-1)((x-1)/x)=tan^(-1)(-7)` , then the value of `x` is (a) 0 (b) -2 (c) 1 (d) 2

Options

A. 2
B. 3
C. 4
D. none of these

Explanation

We know that
`tan^(-1)x+tan^(-1)y=pi+tn^(-1)(x+y)/(1-xy)`
If `xgt0ygt0and xy gt1`
`therefore tan^(-1)(x+1)/(x-1)+tan^(-1)(x-1)/(x-1)xx(x-1)/(x)gt0`
`and ((x+1)/(x-1)+(x-1)/(x))/(1-(x+1)/(x-1)xx(x-1)/(x)=-7`
`rarr x in (-infty,-1)cup(1,infty) and (2x^(2)-x+1)/(1-x)=-7`
`rarr x in(-infty,-1)cup(1,infty) and (x-2)^(2)=0`
`rarr` x=2