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

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)

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

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

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

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

Prove that sin^(-1)(2x.sqrt(1-x^(2)))=2cos^(-1)x,(1)/(sqrt(2))lexlt1