Question

prove this trigonometry identity ​

Answer 1

$lhs = \sqrt{ \frac{1 - cos \alpha }{1 + cos \alpha } } \\ \\ = \sqrt{ \frac{1 - cos \alpha }{1 + cos \alpha } \times \frac{1 - cos \alpha }{1 - cos \alpha } } \\ \\ = \sqrt{ \frac{ {(1 - cos \alpha )}^{2} }{ 1 - {cos}^{2} \alpha } } \\ \\ = \sqrt{ \frac{ {(1 - cos \alpha )}^{2} }{ {sin}^{2} \alpha } } \\ \\ = \frac{1 - cos \alpha }{sin \alpha } \\ \\ = \frac{1}{sin \alpha } - \frac{cos \alpha }{sin \alpha } \\ \\ = cosec \alpha - cot \alpha = rhs$

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Answer 2

Answer:

Proof is given in the attachment.

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