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

Here, `tan^(-1) x + cos^(-1) (y)/(sqrt(1 - y^(2))) = sin^(-1) (3)/(sqrt10)`
`tan^(-1) x + tan^(-1) ((1)/(y)) = tan^(-1) (3)`
`rArr tan^(-1) ((1)/(y)) = tan^(-1) 3 - tan^(-1) (x)`
`rArr tan^(-1) ((1)/(y)) = tan^(-1) ((3 - x)/(1 + 3x))`
`:. y = (1 + 3x)/(3 -x)`
As x, y are positive integers, `x = 1, 2` and corresponding `y = 2, 7`. Therefore, the solution are `(x ,y) = (1, 2) and (2, 7)`, i.e., there are two solution