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

Prove that : tan^(-1) x + cot^(-1) (1+x) = tan^(-1) (1+x+x^2)

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

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

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)))

If x,y are real numbers such that xy<1 then tan^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy))

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

Prove that : tan^(-1)((x-y)/(1+xy)) + tan^(-1)((y-z)/(1+yz)) + tan^(-1)( (z-x)/(1+zx)) = tan^(-1)((x^2-y^2)/(1+x^2y^2))+tan^(-1)((y^2-z^2)/(1+y^2z^2))+tan^(-1)((z^2-x^2)/(1+z^2x^2))

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

Prove that 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x (x != 0)

Prove that tan^(-1)(cot x)+cot^(-1)(tan x)=pi-2x