" 5."cos^(-1)sqrt((1+x)/(2))

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

cos^(-1)(sqrt(1+cos 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)

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 that 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)((2sqrt(x))/(1+x))

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

then -x^(2)=((sqrt(5)-1)/(2)) b.x^(2)=((sqrt(5)+1)/(2)) c.sin(cos^(-1)x)=((sqrt(5)-1)/(2))dtan(cos^(-1)x)=((sqrt(5)-1)/(2))