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The positive integral solution of the equation is

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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