Prove that `|tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot`

Which of the following inequalities are valid- |tan^(-1)x-tan^(-1)y|<=|x-y|AA x,y in R

tan^(-1)x+tan^(-1)y is equal to

Prove that tan^(-1)((x)/(y))-tan^(-1)((x-y)/(x+y)) is (pi)/(4) and Not(-3 pi)/(4)

Formula for tan^(-1)(x)+-tan^(-1)(y)

If x=2. y=3 , then tan^(-1)x+tan^(-1)y=

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)))))

If tan^(-1)y=4tan^(-1)x , then 1//y is zero for

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