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

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

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

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

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

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

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

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

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

Prove the followings : cos^(-1)x=2sin^(-1)sqrt((1-x)/2)=2cos^(-1)sqrt((1+x)/2)