[" (ix) cos "^(-1)(sqrt((1+x)/(2)))],[" stations method: "]

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

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

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

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

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

(1) / (2) cos ^ (- 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 sqrt(3)+cos^(-1)x=(pi)/(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)

lim _(x to ((1)/(sqrt2))^(+))(cos ^(-1) (2x sqrt(1- x ^(2))))/((x-(1)/(sqrt2)))- lim _(x to ((1)/(sqrt2))^(-))(cos ^(-1) (2x sqrt(1-x ^(2))))/((x- (1)/(sqrt2)))=

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