prove that `cot^-1[sqrt((1+cos3x)/(1-cos3x))]`

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

If pi

If x in (pi, 2pi) , prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(1+cos x)) -sqrt(1-cos x)) = cot(pi/4 +x/2)

Prove that: sqrt ((1 + cos A) / (1-cos A)) = cos ecA + cot A

Prove that: (i)tan^(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=(pi)/(4)+(x)/(2)

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))

Prove that : cot^(-1) ((sqrt(1+x) -sqrt(1-x))/(sqrt(1+x) +sqrt(1-x))) = pi/4 +1/2 cos^(-1) x

Prove that cot^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)+(1)/(2)cos^(-1)x

Prove that: tan^(^^)(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=pi/4-x/2, if pi