Q. 5

# Choose the correc

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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