If \( a=(\cos \theta+i \sin \theta) \), prove that \( \frac{1+a}{1-a}=\left(\cot \frac{\theta}{2...

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If \( a=(\cos \theta+i \sin \theta) \), prove that \( \frac{1+a}{1-a}=\left(\cot \frac{\theta}{2}\right) i \).
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