[" Prove that "tan^(-1)[(sqrt(1)+cos x+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))]=(pi)/(4)-(x)/(2)," where "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-cosx))/(sqrt(1+cos x)-sqrt(1-cosx))}=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

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)

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)

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) .

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

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1