prove that `tan^-1(cosx/(1-sinx))-cot^-1(sqrt(1+cosx)/sqrt(1-cosx))=pi/4 , xepsilon(0,pi/2)`

Prove that : tan^(-1)((cosx)/(1-sinx))-cot^(-1)(sqrt((1+cosx)/(1-cosx)))=(pi)/(4), x in (0, pi//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: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2 ,

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

Prove that: tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2,\ if\ pi < x <\3pi/2

Prove that tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)

If pi < x < 2pi, prove that (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))="cot(x/2+pi/4)dot

If pi < x < 2pi, prove that (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))="cot(x/2+pi/4)dot

If pi < x < 2pi, prove that (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))="cot(x/2+pi/4)dot

If piltxlt2pi, prove that (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))=cot(x/2+pi/4)dot