Question

If `tan^-1x + tan^-1y = pi/4`, then ______

पर्याय

• x + y + xy = 1

• x + y - xy = 1

• x + y + xy + 1 = 0

• x + y - xy + 1 = 0

Answer 1

If `tan^-1x + tan^-1y = pi/4`, then x + y + xy = 1.

Explanation:

Given, `tan^-1x + tan^-1y = pi/4`

⇒ `tan^-1((x + y)/(1 - xy)) = tan^-1`

⇒ `(x + y)/(1 - xy) = 1 ⇒ x + y + xy = 1`