Question

please answer fast 1+sin theta/cosec theta-cot theta - 1 - sin theta/cosec theta +cot theta =2(1+cot theta) prove ​

Answer 1

Answer:

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Answer 2

$\frac{1 + sin \theta}{cosec \theta - cot \theta} - \frac{1 - sin \theta}{cosec \theta + cot \theta} \\ \\ = \frac{sin \theta(1 + sin \theta)}{1 - cos \theta} - \frac{sin \theta(1 - sin \theta)}{1 + cos \theta}$

$= sin \theta (\frac{1 + cos \theta + sin \theta + sin \theta cos \theta - 1 + cos \theta + sin \theta - sin \theta cos \theta}{ {sin}^{2} \theta} ) \\ \\ = \frac{2(sin \theta + cos \theta)}{sin \theta} \\ \\ = 2(1 + cot \theta)$