Question

If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.

Options

• π

• `pi/5`

• `(2pi)/5`

• `(3pi)/5`

Answer 1

If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals `pi/5`.

Explanation:

`cot^-1x + cot^-1y`

= `(pi/2 - tan^-1x) + (pi/2 - tan^-1y)`  ......[`[because tan^-1x + cot^-1x = pi/2]`

= `pi - (tan^-1x + tan^-1y)`

= `pi - (4pi)/5`

= `pi/5`