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If x < 0, y < 0 such that xy = 1, then tan–1x + tan–1y equals
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