`a r c t a n^(- 1)((cosx)/(1-sinx))-cos^(- 1)(sqrt((1+cosx)/(1-cosx)))=pi/4, x in (0,pi/2)`

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

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

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

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

Show that: tan^(-1)[ (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))] =(pi)/(4)+(x)/(2), x in [0, pi]

cos^(-1)((sinx+cosx)/(sqrt(2))),-(pi)/(4) ltx lt(pi)/(4)