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

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

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

Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) cos [tan^(-1) (cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

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

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

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

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