Trig

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How do I prove that

tan(x/2) =( plus/minus) sqrt(1-cos(x/1+cos(x))

  • Trig -

    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

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