" 15."cos^(-1){sqrt((1+x)/(2))}

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

Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x lt 1

Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x lt 1

Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x lt 1

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

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

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))

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