The value of `tan(2tan^(-1)(1/5))`

Explanation

=`tan(2tan^-1 1/5) `

as `[2 tan^-1 x = tan^-1((2x)/(1-x^2))]`

so,`tan(tan^-1 ((2(1/5))/(1- (1/5)^2)))`

`= tan(tan^-1 (2/5 xx 25/24))`

`= 5/12`

Answer