Question

(cosecθ + cotθ)² = 1-cosθ / 1+cosθ

Prove that...

Answer 1

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Answer 2

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