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

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

prove that . Tan ^(-1) x- tan ^(-1 )y = cos ^(-1) (1+xy)/(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))))

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))))

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

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)))) .

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

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