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)))`

Find the number of positive integral solution of the equation `tan^(-1

1.	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)))`
Answer» `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`. When `x = 1, y= (1+3)/2 => y= 2` When `x = 2, y= (1+6)/1 => y= 7` So, these are two possible solutions for the given equation.

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