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Math Help - half angle formulae question

  1. #1
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    half angle formulae question

    How do I prove that ( (1-cos A) / (1+cos A) ) = (tan (A/2))^2 ?

    I have tried using the half angle formulae for cos A but have not entirely finished the question.
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  2. #2
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    Quote Originally Posted by Stuck Man View Post
    How do I prove that ( (1-cos A) / (1+cos A) ) = (tan (A/2))^2 ?

    I have tried using the half angle formulae for cos A but have not entirely finished the question.
    \displaystyle \tan^2\left(\frac{A}{2}\right) = \frac{\sin^2\left(\frac{A}{2}\right)}{\cos^2\left(  \frac{A}{2}\right)} = \frac{\frac{1-\cos{A}}{2}}{\frac{1+\cos{A}}{2}} = \frac{1-\cos{A}}{1+\cos{A}}
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  3. #3
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    Thats much shorter than I expected. I used the 'little t' formula for cos A. Thanks.
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