We are given that,

xy = 1, x < 0 and y < 0

We need to find the value of tan^-1 x + tan^-1 y.

Using the property of inverse trigonometry,

We already know the value of xy, that is, xy = 1.

Also, we know that x, y < 0.

Substituting xy = 1 in denominator,

And since (x + y) = negative value = integer = -a (say).

⇒ tan^-1 x + tan^-1 y = tan^-1 -∞ …(i)

Using value of inverse trigonometry,

Substituting the value of tan^-1 -∞ in the equation (i), we get