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Simple triganomic identity

  1. Mar 22, 2005 #1
    Nothing special, i'm just not clicking on this question

    [tex]\frac {1-\cos\theta}{\sin\theta} = \tan \frac {a}{2}[/tex]

  2. jcsd
  3. Mar 22, 2005 #2
    I'm going to assume by [itex]a[/itex] you mean [itex]\theta[/itex].

    In that case, use

    [tex]\cos^2{u} = \frac{1}{2}(1+ \cos{2u})[/tex]


    [tex]\sin^2{u} = \frac{1}{2}(1 - \cos{2u})[/tex]

    [tex] \Longrightarrow \tan^2{u} = \frac{1 - \cos{2u}}{1 + \cos{2u}}[/tex]

    to get rid of the annoying [tex]\frac{\theta}{2}[/tex], and then multiply by an appropriate version of 1.
  4. Mar 22, 2005 #3


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    [tex] \sin\theta=2\sin\frac{\theta}{2}\cos\frac{\theta}{2} [/tex]

    [tex] 1-\cos\theta=2\sin^{2}\frac{\theta}{2} [/tex]

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