Question

(Cosec∅ - Cot∅)² = 1- Cos∅/ 1+ Cos∅​

Answer 1

Step-by-step explanation:

$( \cos( \alpha ) - \cot( \alpha )) {}^{2}$

$= ( \frac{1}{ \sin( \alpha ) } - \frac{ \cos( \alpha ) }{ \sin( \alpha ) } ) {}^{2}$

$= ( \frac{1 - \cos( \alpha ) }{ \sin( \alpha ) } ) {}^{2}$

$\\ = \frac{(1 - \cos( \alpha ) ) {}^{2} }{ \sin {}^{2} ( \alpha ) {} }$

$= \frac{(1 - \cos( \alpha ) )}{1 - \cos {}^{2} ( \alpha ) }$

$= \frac{(1 - \cos( \alpha ) ) {}^{2} }{(1 - \cos( \alpha ))(1 + \cos( \alpha ) )}$

$= \frac{1 - \cos( \alpha ) }{1 + \cos( \alpha ) }$

Answer 2

Step-by-step explanation:

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