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Math Help - Half-Angle Identity

  1. #1
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    Half-Angle Identity

    How would you do from \frac{\sin \theta}{2-2 \cos \theta} to \frac{1}{2} \cot \left( \frac{ \theta }{2} \right) ?

    I tried it for a while but the squaring in the \cos identity is causing confusion. Thank in advance.
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  2. #2
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    \cot \frac{\theta}{2} = \pm\, \sqrt\frac{1 + \cos \theta}{1 - \cos \theta} = \frac{1 + \cos \theta}{\sin \theta} = \frac{\sin \theta}{1 - \cos \theta} = \csc \theta + \cot \theta.\,

    (From Wikipedia. )
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