`cot^-1x=tan^-1x` then -

int\ (tan^(-1)x - cot^(-1)x)/(tan^(-1)x + cot^(-1)x) \ dx equals

If cot^-1 x = tan^-1(1/x) for all x in S, then find the set S.

If y=(tan^(-1)x-cot^(-1)x)/(tan^(-1)x+cot^(-1)x) then (dy)/(dx)=

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

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

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

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

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

Prove that tan(cot^-1x) = cot(tan^-1x) . State with reason whether the equality is valid for all values of x.