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Oh those identities!

  1. Mar 4, 2008 #1
    Anyone know if the difference of cos^2 and sin^2 is some obscure identity that no one's heard of?

    Edit: nevermind. Shaum's tells me that cos^2 - sin^2 = cos(2a). GO SHAUMS!!
     
    Last edited: Mar 4, 2008
  2. jcsd
  3. Mar 5, 2008 #2

    HallsofIvy

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    So the answer to your question is "NO"! It is, in fact, a well known identity!

    A more general identity is cos(x+ y)= cos(x)cos(y)- sin(x)sin(y). Letting x= y= a in that, cos(2a)= cos2(a)- sin2(a).
     
  4. Mar 5, 2008 #3
    If you know complex numbers [including de Moivre's theorem (great chap, wasn't he) and Binomial Theorem], you can find the exact angle of any sin/cos/tan in surd form, and you can prove any double angle/triple angle/quadruple angle etc angles.

    Back on topic though, yes those identities are very famous, and cos^2+sin^2 = 1 is also a darned famous one, think Pythagoras. From that you can get 2 more forms, one with sec and the other with csc
     
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