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

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)

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

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

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

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

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

Number ofsolution(s) ofthe equation cos^(-1)sqrt(x)-sin^(-1)sqrt(x-1)+cos^(-1)sqrt(1-x)-sin^(-1)((1)/(sqrt(x)))=(pi)/(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))