Answer :

We need to find the positive integral solution of the equation:


Using property of inverse trigonometry,



Also,



Taking,









Using the property of inverse trigonometry,



Similarly,



Taking tangent on both sides of the equation,



Using property of inverse trigonometry,


tan(tan-1 A) = A


Applying this property on both sides of the equation,



Simplifying the equation,





Cross-multiplying in the equation,


xy + 1 = 3(y – x)


xy + 1 = 3y – 3x


xy + 3x = 3y – 1


x(y + 3) = 3y – 1



We need to find positive integral solutions using the above result.


That is, we need to find solution which is positive as well as in integer form. A positive integer are all natural numbers.


That is, x, y > 0.


So, keep the values of y = 1, 2, 3, 4, … and find x.



Note that, only at y = 2, value is x is positive integer.


Thus, the positive integral solution of the given equation is x = 1, y = 2.

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