prove that `. Tan ^(-1) x- tan ^(-1 )y = cos ^(-1) (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 sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))

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

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

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

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) (1+y^2))))

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