Answer :

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


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