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))*sqrt(1+y^(2))))

tan^(-1)((x)/(y))-tan^(-1)((x-y)/(x+y)) is

Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))="sin"^(-1)((y-x)/(sqrt(1+x^(2))sqrt(1+y^(2)))) .

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

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

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

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

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

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