Question

Evaluate:

`sin(tan^-1x+tan^-1  1/x)` for x > 0

Answer 1

`sin(tan^-1x+tan^-1  1/x)`

`=sin(tan^-1x+cot^-1x)`      `[thereforetan^-1x=cot^-1  1/x]`

`=sin(pi/2)`                    `[thereforetan^-1x=cot^-1x=pi/2]`

= 1