How do I prove that
tan(x/2) =( plus/minus) sqrt(1-cos(x/1+cos(x))
not true, if you meant:
tan(x/2) =( plus/minus) sqrt(1-cos(x/(1+cos(x)))
let x = 2 radians
LS = tan 1 = appr 1.557
RS = ± √(1 - cos( 2/(1 + cos 2)
let's look at cos (2/(1+ cos2)
= cos(2/.58385)
= cos(3.4255) = -.95996
so RS = ± √( 1 - (-.95996) = ±√1.95996 = ± 1.4
≠ LS
If done the way you typed it
LS = tan 1 = appr 1.557
RS = ±√(1 - cos(2/1 + cos2)
= ± √( 1 - cos(1.5868..)) = ± 1.0065 ≠ LS
so check your equation, or your typing