Find the value of `tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))`

If x<0,\ y<0 such that x y=1 , then write the value of tan^(-1)x+tan^(-1)y .

Find the value of: tan(1/2 [sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))]),|x| 0 and x y < 1

If x + y + z = xyz and x, y, z gt 0 , then find the value of tan^(-1) x + tan^(-1) y + tan^(-1) z

Find the value of: tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)(1-y^2)/(1+y^2)],|x| 0 and x y" "<" "1

Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt((1+x^2) (1+y^2))))

Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt((1+x^2)(1+y^2))))

For x,y,z,t in R , if sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)*t+3pi , then the value of tan^(-1)x+tan^(-1)y+tan^(-1)z+tan^(-1)( sqrt((2)/(pi))t) is __________.

The result tan^(-1)x-tan^(-1)y = tan^(-1)((x-y)/(1+xy)) is true when the value of xy is "………."

If x and y are positive integer satisfying tan^(-1)((1)/(x))+tan^(-1)((1)/(y))=(1)/(7) , then the number of ordered pairs of (x,y) is

Prove that : tan^(-1)((x-y)/(1+xy)) + tan^(-1)((y-z)/(1+yz)) + tan^(-1)( (z-x)/(1+zx)) = tan^(-1)((x^2-y^2)/(1+x^2y^2))+tan^(-1)((y^2-z^2)/(1+y^2z^2))+tan^(-1)((z^2-x^2)/(1+z^2x^2))