If `r^2 = x^2 + y^2 + z^2` , then prove that `tan^(-1)((yz)/(rx))+tan^(-1)((zx)/(ry))+tan^(-1)((xy)/(rz))=pi/2`

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

Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))

Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4

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

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to pi (b) pi/2 (c) 0 (d) none of these

tan ^(-1) ""(1)/(x)+tan ^(-1) ""2=(pi)/(2)

Prove that, "tan"^(-1)(1)/(2xx1^(2))+"tan"^(-1)(1)/(2xx2^(2))+"tan"^(-1)(1)/(2xx3^(2))+…oo=(pi)/(4)

Prove that, tan^(-1)((3 sin 2x)/(5+3 cos 2x))+tan^(-1)((1)/(4) tan x)=x .

Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A) =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 ne 0