Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 5 of MCQ
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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.
