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 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 (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))=cot(a+x/2) and x in (pi,2pi) then 'a' is equal to :

int(sqrt(1+cosx))/(1-cosx)dx=

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

intcot^(-1)sqrt((1+cosx)/(1-cosx))dx=

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

Evaluate int_0^(pi/2) sqrt(cosx)/(sqrt(cosx)+sqrt(sinx))dx

int_(0)^(pi//2)(sqrt(cosx))/((sqrt(cosx)+sqrt(sinx)))dx=?

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:

Prove that tan^(-1)(sqrt((1-cosx)/(1+cosx))=x/2, x lt pi .