Find the number of positive integral solutions of `tan^-1 x + cot^-1 y = tan^-1 3`.

The number of positive integral solutions of tan^(-1)x + cot^(-1)y= tan^(-1)3 is :

STATEMENT-1 : If tan^2 (sin^-1x) > 1 then x in(-1-1/sqrt2)uu(1/sqrt(2).1).STATEMENT-2 : The number of positive integral solution of tan^-1 1/y+cot^-1(1/x)=cot^-1(1/3), where x/y < 1, is 2. STATEMENT -3 : If sin^-1 x=-cos^-1 sqrt(1-x^2) and sin^-1 y=cos^-1 sqrt(1-y^2), then the exact range of (tan^-1 x+ tan6-1 y) is [-pi/4,pi/4].

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)x+(cos^(-1)y)/(sqrt(1+y^(2)))=(sin^(-1)3)/(sqrt(10))

Find the number of solution of 2 tan^(-1) (tan x) = 6 - x

Find the number of positive integral solutions satisfying the equation (x_(1)+x_(2)+x_(3))(y_(1)+y_(2))=77

If k be a positive integer , show that the equation tan^-1 x+tan^-1 y= tan^-1 k has no positive integral solution.

The number of real solution of equation tan^(-1)x+cot^(-1)(-|x|)=2tan^(-1)(6x) is