The numerical value of `"tan"(2tan^(-1)(1/5)-pi/4` is equal to____

Answer

`(- (7)/(17))`

Explanation

` tan [ 2 tan ^(-2) ((1)/(5)) - (pi)/(4)] = tan [ tan ^(-1) (( 2* (1)/(5))/( 1 - ( 1)/( 25))) - (pi)/(4)]`
`" "= tan [ tan ^(-1) ((5)/( 12)) - (pi)/( 4)] `
` " " = ( tan [ tan ^(-1) ((5)/( 12)) ] - tan (( pi)/( 4)))/( 1 + tan [ tan ^(-1) ((5)/( 12)) ] tan ""(pi)/( 4))`
` " " = ((5)/( 12) - 1 )/( 1 + ( 5)/( 12) * 1) = - ( 7)/( 17)`