Question

1/1- cos theta-1/1+cos theta=2 cot theta. cosec theta
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Answer 1

Refer the attachment

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Answer 2

$\frac{1}{1 - cos \theta} - \frac{1}{1 + cos \theta} \\ \\ = \frac{1 + cos \theta - 1 + cos \theta}{1 - {cos}^{2} \theta} \\ \\ = \frac{2cos \theta}{ {sin}^{2} \theta } \\ \\ = 2cot \theta \: cosec \theta$