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

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

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

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 cos^(-1)x=2sin^(-1)(sqrt (1-x)/sqrt2)

If 1/(sqrt(2))

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

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

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

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

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