हल करे :
`tan^(-1)"" (1-x)/(1+x) = (1)/(2) tan^(-1) x(x gt 0)`

Explanation

दिया है, `tan^(-1) x = 2 tan^(-1) ((1-x)/(1+x))`
` = tan^(-1) ""(2((1-x)/(1+x)))/(1-((1-x)/(1+x))^(2))" "[because 2 tan^(-1) x = tan^(-1)""(2x)/(1-x^(2))]`
`= tan^(-1)""(2(1-x)(1+x))/((1+x)^(2)-(1-x)^(2))`
`= tan^(-1) ""(2(1-x^(2)))/(4x)`
`therefore tan^(-1) x = tan^(-1)"" (1-x^(2))/(2x)`
`therefore x = (1-x^(2))/(2x) " "[because tan^(-1)` एकैकी फलन है]
`rArr 2x^(2) = 1-x^(2) " " rArr 3x^(2) = 1`
`rArr x = pm (1)/(sqrt(3)) " " therefore x = (1)/(sqrt(3))" "[because x gt 0]`