" 38.Prove that "tan(cot^(-1)x)=cot(tan^(-1)x)

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

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

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

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

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

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

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

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

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