Question

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

विकल्प

• `pi/5`

• `(2pi)/5`

• `(3pi)/5`

• π

Answer 1

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

Explanation:

We have, tan^–1x + tan^–1y = `(4pi)/5`

⇒ `pi/2 - cot^-1x + pi/2 - cot^-1y = (4pi)/5`

⇒ `pi- (cot^-1x + cot^-1y) = (4pi)/5`  .....`(because tan^-1x + cot^-1x = pi/2)`

⇒ `cot^-1x + cot^-1y = pi - (4pi)/5`

⇒ `cot^-1x + cot^-1y = pi/5`