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

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

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

Prove that , tan^(-1)""x+ tan^(-1) ""y+tan^(-1)""z= tan ^(-1)""(x+y+z-xyz)/(1-xy-yz-zx)

If tan ^(-1 )""(yz )/( xr ) + tan ^(-1 )""(zx)/(yr) + tan ^(-1) ""(xy)/(zr) =(pi)/(2) , prove that , x^(2) + y^(2) + z^(2) + r^(2)

tan (cos ^(-1) x) = sin (cot ^(-1) ""(1)/(2))

prove that cos tan ^(-1) ""sin cot ^(-1) ""x=((x^(2)+1)/(x^(2)+2))^(1/2)

cot^(-1)""(xy+1)/(x-y)+cot^(-1)""(yz+1)/(y-z) +cot ^(-1) "" (zx +1)/(z-x)=0

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

Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1/(sqrt(3))

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