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Math Help - Trig problem

  1. #1
    Junior Member
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    Trig problem

    Show that \frac{1-cos2x}{1+cos2x}=tan^2x
    and hence find the exact value of tan22.5
    Last edited by requal; September 5th 2009 at 01:43 AM. Reason: typo
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  2. #2
    Junior Member
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    Aug 2009
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    Gothenburg, Sweden
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    From the formulas \cos 2x = \cos^2 x -\sin^2 x and \sin^2 x + \cos^2 x =1:
    LHS= \frac{1-\cos 2x}{1+\cos 2x}=\frac{1-\cos^2 x +\sin^2 x}{1+ \cos^2 x -\sin^2 x}=\frac{2\sin^2 x}{2\cos^2 x}=\tan^2 x=RHS.
    Now plug in x=22.5 and solve for \tan 22.5.
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