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Proving this trigonometric identity

  1. Feb 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove the following identity: [tex](1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta)[/tex]

    2. Relevant equations

    [tex]cos^2 \theta + sin^2 \theta = 1[/tex]

    3. The attempt at a solution

    I've squared out the first bracket so that it becomes [tex]1 + cos^2 \theta[/tex] and multiplied out the second bracket so that it becomes [tex]2 + 2cos \theta[/tex]. With some rearrangement I get [tex]cos^2 \theta + sin^2 \theta = 1 + 2cos \theta[/tex]

    I can't get rid of the 2cos, and I think it's because I'm doing something wrong when squaring out that first bracket. But I can't see what it is that I'm doing wrong, only that [tex]1 + cos^2 \theta[/tex] doesn't = [tex](1 + cos \theta)^2[/tex].

    What am I doing wrong?
     
  2. jcsd
  3. Feb 18, 2007 #2

    cristo

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    [tex](1+\cos\theta)^2=1+2\cos\theta+\cos^2\theta[/itex]
     
  4. Feb 18, 2007 #3
    Ahh thank you! Looks like I forgot a very simple rule of algebra. I hate it when that happens XD.
     
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