" ample "1" 4.Prove that "cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))

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

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

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

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

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

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

prove that 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))

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))

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))