Prove that: `cos^(-1)[sqrt((1+cosx)/2)]=x/2`

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

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

Prove that tan^(-1)(sqrt((1-cosx)/(1+cosx))=x/2, x lt pi .

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

Differentiate the following with respect to x cos^(-1) sqrt((1+cosx)/2)

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

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

Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2 ,

Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2 ,

Prove that: tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2,\ if\ pi < x <\3pi/2