tan^(-1)((cos x)/(1-sin))-cot^(-1)(sqrt((1+cos)/(1-cos)))=(pi)/(4)quad x in(0,pi/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 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: (i)tan^(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=(pi)/(4)+(x)/(2)

cos^(-1)((sin x+cos x)/(sqrt(2))),(pi)/(4) lt x lt (5pi)/4

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)

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

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:

Differentiate tan^(-1) sqrt((1-cos x)/(1 + cos x)), - (pi)/(4) lt x lt (pi)/(4)

If pi