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

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){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=pi/4-x/2, if pi

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

Directions Prove the following "tan"^(-1)((sqrt(1+"cos"x)+sqrt(1-"cos"x))/(sqrt(1+"cos"x)-sqrt(1-"cos"x)))=pi/(4)+x/(2) , if piltxlt(3pi)/(2) .

tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)}}=(pi)/(4)+(x)/(2) , 0 lt x lt (pi)/(2)

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

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

Simplest form of tan^(-1)((sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))), pi lt x lt (3 pi)/(2) is:

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)

If pi