" (iii) "lan^(-1)(1)/(x+y)+tan^(-1)(y)/(x^(2)+xy+1)=cot^(-1)x

tan^(- 1) (1/(x+y)) +tan^(- 1) (y/(x^2+x y+1)) =cot^(- 1)x

Prove that tan ^(-1)""(1)/(x+y)+ tan ^(-1)""(y)/(x^(2)+xy+1)= cot ^(-1)x.

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

Prove the "tan"^(-1) 1/(x+y) + "tan"^(-1) y/(x^2=xy+1) ="tan"^(-1)1/x

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

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

If xy=1 + a^(2) then show that tan^(-1) ""(1)/(a+x)+tan ^(-1) ""(1)/(a+y)=tan ^(-1)""(1)/(a) , x+y+2a ne 0

If xy=1+a^(2) then show that tan^(-1)((1)/(a+x))+tan^(-1)((1)/(a+y))=tan^(-1)((1)/(a)),x+y+2a!=0

If x gt y gt z gt 0 , then find the value of "cot"^(-1) (xy + 1)/(x - y) + cot^(-1).(yz + 1)/(y - z) + cot^(-1).(zx + 1)/(z - x)

Prove that following cot^(-1)((xy+1)/(x-y)) +cot^(-1)((yz+1)/(y-z))+cot^(-1)((zx+1)/(z-x))=0, (0 lt xy, yz, zx lt 1)