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

`tan^-1x+cos^-1(y/(1+y^2)) = sin^-1(3/sqrt10)`

We will convert this equation in `tan^-1` form.

`=> tan^-1x + tan^-1(1/y) = tan^-1 3`

`=>tan^-1(1/y) = tan^-1 3 - tan^-1 x`

`=>tan^-1(1/y) = tan^-1((3-x)/(1+3x))`

`=>1/y = (3-x)/(1+3x)`

`=> y = (1+3x)/(3-x)`

As, we have to find positive integral values, so `x` can have only two values, `1` and `2`.

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