Find the number of positive integral solution of the equation `tan^(-1)x+cos^(-1)(y/(sqrt(1+y^2)))=sin^(-1)(3/(sqrt(10)))`

Explanation

To solve the equation \( \tan^{-1} x + \cos^{-1} \left( \frac{y}{\sqrt{1+y^2}} \right) = \sin^{-1} \left( \frac{3}{\sqrt{10}} \right) \), we will follow these steps:

### Step 1: Rewrite the equation using trigonometric identities
We know that:
\[ \cos^{-1} \left( \frac{y}{\sqrt{1+y^2}} \right) = \tan^{-1} \left( \frac{1}{y} \right) \]
This is because if we take a right triangle where the opposite side is 1 and the adjacent side is \( y \), then the hypotenuse will be \( \sqrt{1+y^2} \).
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