Question

Evaluate the following:

`tan{2tan^-1  1/5-pi/4}`

Answer 1

`tan{2tan^-1  1/5-pi/4}`

`= tan [tan^-1 (2xx1/5)/(1-(1/5)^2) - tan^-1 1]`

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

`= tan[tan^-1 10/24 - tan^-1]`

`= tan [(tan^-1  10/24 - 1)/(1+ 10/24 xx1)]`

`= tan [tan^-1  (10-24/24)/(24+10/24)]`

`=tan [tan^-1 -14/34]`

`= tan [tan^-1 -7/17]`

`= -7/17`