Prove that `costan^(-1)sin cot^(-1)x=sqrt((x^2+1)/(x^2+2))`

If x lt 0 , then prove that cos^(-1)x=pi+tan^(-1)""(sqrt(1-x^2))/x

Prove that tan ^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))=pi/4+1/2 cos ^(-1) x^2

Prove that tan ^(-1) x+tan ^(-1) ((2 x)/(1-x^2))=tan ^(-1)((3 x-x^3)/(1-3 x^2)),|x|lt1/sqrt3

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

Prove that cos^-1x=2sin^-1sqrt((1-x)/2)

The value of cos [ tan^-1 {sin (cot^-1 (x))}] is a) sqrt((x^2+1)/(x^2-1)) b) sqrt((1-x^2)/(x^2+2)) c) sqrt((1-x^2)/(1+x^2)) d) sqrt((x^2+1)/(x^2+2))

prove that tan^(-1) sqrt x = 1/2 cos^(-1)((1-x)/(1+x)), x in [0,1]

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

int_0^1 (sin ^(-1) x)^3/(sqrt(1-x^2 ))d x

Prove : tan^-1x=sec^-1sqrt(1+x^2) .