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

arctan^(-1)((cos x)/(1-sin x))-cos^(-1)(sqrt((1+cos x)/(1-cos x)))=(pi)/(4),x in(0,(pi)/(2))

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

prove that tan^(-1)((cos x)/(1-sin x))-cot^(-1)((sqrt(1+cos x))/(sqrt(1-cos x)))=(pi)/(4),x varepsilon(0,(pi)/(2))

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

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

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))

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))

tan ^(-1)(sqrt((1-cos 3 x)/(1+cos x)))

cos^(-1){sqrt(1-x^(2))}