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

Prove that: tan(x/2)=pmsqrt[(1-cosx)/(1+cosx)]

Prove that 2 tan^-1 sqrt((1- x)/(1+x))= x, -1 le x le 1

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

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

Evaluate: (i) intsin^(-1)(cosx)\ dx ,\ \ 0lt=xlt=pi (ii) inttan^(-1){sqrt(((1-cos2x)/(1+cos2x)))}\ dx ,\ \ 0 le x le pi//2

Prove that tan^(-1)((sqrt(1-x^(2)))/(1+x))=(1)/(2)cos^(-1)x

Write the following functions in the simplest form: tan^-1((sqrt(1-cosx)/(1+cosx)), 0 < x< pi

Prove that tan^(-1) x + tan^(-1).(1)/(x) = {(pi//2,"if" x gt 0),(-pi//2," if " x lt 0):}

Prove that tan^(-1)((x)/(1+sqrt(1-x^(2))))=(1)/(2)sin^(-1)x .