Prove that `cos^(-1){sqrt((1+x)/2)}=(cos^(-1)x)/2`

cos^(-1)(sqrt((1+cos x)/2))

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

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

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

Prove that cos^(-1) (sqrt(1/3))-cos^(-1) (sqrt((1)/(6)))+cos^(-1) ((sqrt(10)-1)/(3sqrt2))=cos^(-1) (2/3)

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

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x) = (pi)/(2), |x| le 1

Prove that : cos^(-1) x + cos^(-1) ((x)/(2) + (sqrt( 3-3x^2) )/( 2) ) = (pi)/ (3)

Prove that sin^(-1) {(sqrt(1 + x) + sqrt(1 - x))/(2)} = (pi)/(4) + (cos^(-1) x)/(2), 0 lt x lt 1

Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1