If `sin^(-1)((2a)/(1+a^(2)))-cos^(-1)((1-b^(2))/(1+b^(2)))=tan^(-1)((2x)/(1-x^(2)))`, then what os the value of x ?

Options

A. a/b
B. ab
C. b/a
D. `(a-b)/(1+ab)`

Answer

D

Explanation

Given, `sin^(-1)((2a)/(1+a^(2)))-cos^(-1)((1-b^(2))/(1+b^(2)))=tan^(-1)((2x)/(1-x^(2)))`
`therefore 2 tan^(-1) a - 2 tan^(-1)b = 2 tan^(-1)x`
`rArr tan^(-1)a-tan^(-1)b=tan^(-1)x`
`rArr tan^(-1)((a-b)/(1+ab))=tan^(-1)x`
`rArr x = (a-b)/(1 + ab)`