सिद्ध करे कि :
`tan^(-1) x + tan^(-1) y = (1)/(2)sin^(-1) ""(2(x+y)(1-xy))/sqrt((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) x- tan ^(-1 )y = cos ^(-1) (1+xy)/(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 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))))

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))))

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

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{(1/2)sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))} .