Question

`tan[2tan^-1 (1/3) - pi/4]` = ______.

Options

• `1/7`

• `-1/7`

• `17/7`

• `-17/7`

Answer 1

`tan[2tan^-1 (1/3) - pi/4]` = `-1/7`.

Explanation:

`tan[2tan^-1 (1/3) - pi/4]`

= `tan[tan^-1 ((2/3)/(1 - 1/9)) - tan^-1 (1)]`  .......`[because 2tan^-1 x = tan^-1((2x)/(1 - x^2))]`

= `tan[tan^-1 (3/4) - tan^-1 (1)]`

= `tan[tan^-1  ((3/4 - 1)/(1 + 3/4))]`

= `tan[tan^-1 (-1/7)]`

= `-1/7`