Question

Write the value of tan⁻¹x + tan⁻¹ `(1/x)`for x > 0.

Answer 1

`tan^-1x+tan^-1y=tan^-1((x+y)/(1-xy)), xy<1`

`thereforetan^-1x+tan^-1  1/x=tan^-1((x+1/x)/(1-x  1/x)),x>0`

`=tan^-1((x^2+1)/0)`

`=tan^-1 (oo)`

`=tan^-1(tan  pi/2)`

`=pi/2`

 

`thereforetan^-1x+tan^-1  1/x=pi/2`