Question

(cosecø-cotø)²@=1-cosø/1+cosø​

Answer 1

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

Hence Proved.