`tan^(-1)""(x)/(y)-tan^(-1)""(x-y)/(x+y)`

Prove that tan ^(-1)""(1)/(x+y)+ tan ^(-1)""(y)/(x^(2)+xy+1)= cot ^(-1)x.

Statement -I : tan ^(-1)""((3)/(4))+tan ^(-1) ""((1)/(7))= (pi)/(4) statement -II: "for" x gt 0 , y gt 0 tan^(-1 ) ((x)/(y))+tan^(-1)""((y-x)/(y+x))=(pi)/(4)

Statement 1: tan^(-1)((3)/(4))+tan^(-1)((1)/(7))=(pi)/(4) Statement 2: For x gt 0, Y gt 0 tan^(-1)((x)/(y))+tan^(-1)((y-x)/(y+x))=(pi)/(4)

Statement 1: tan^(-1)((3)/(4))+tan^(-1)((1)/(7))=(pi)/(4) Statement 2: For x gt 0, Y gt 0 tan^(-1)((x)/(y))+tan^(-1)((y-x)/(y+x))=(pi)/(4)

tan ^(-1)((1)/(x+y))+tan ^(-1)((y)/(x^(2)+x y+1))=

Prove that tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy)),xygt-1

tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy)) holds good for

tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy)) holds good for

If x,y are real numbers such that xy<1 then tan^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy))