Posted by **Sarah** on Sunday, January 27, 2013 at 1:28pm.

How do I prove that

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

- Trig -
**Reiny**, Sunday, January 27, 2013 at 4:00pm
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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