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Homework Help: Prove trigonometric equality: 1 - cosx = 2(sin^2)*(x/2)

  1. Aug 11, 2014 #1
    1. The problem statement, all variables and given/known data

    It seems like a pretty straightforward equality but I when I tried to google it doesn't seem like it is known at all. All the paths I have tried have been dead ends.

    The question was initially:

    Find the limit as x approaches 0 for the expression (1-cosx)/x^2

    In the second step of the solution, the expression became (2(sin^2)*(x/2)) / x^2 and I didn't know how the numerator changed to that new expression.

    Thank you for your help!
  2. jcsd
  3. Aug 11, 2014 #2


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    Do you know the identity ##\cos(2x)= \cos^2x - \sin^2x = 1-2\sin^2x##? Solve for ##1-\cos(2x)## in terms of ##\sin^2x## and replace ##x## by ##\frac\theta 2## and you will have the identity you are looking for.
    Last edited: Aug 11, 2014
  4. Aug 11, 2014 #3
    Thank you that was exactly what I needed!
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