Question

Prove it :-
$\frac{ \cos( \alpha ) }{1 - \sin( \alpha ) } = \frac{1 + \sin( \alpha ) }{ \cos( \alpha ) }$
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Answer 1

Refer to the above attachment.

Answer 2

$Question:-</h2><p></p><h2> \\ \frac{ \cos( \alpha ) }{1 - \sin( \alpha ) } = \frac{1 + \sin( \alpha ) }{ \cos( \alpha ) } \\ Answer:- \\ LHS:- \\ = \frac{cos \alpha }{1 - sin \alpha } \\ = \frac{cos \alpha \times (1 + sin \alpha }{1 - sin \alpha \times (1 + sin \alpha ) } \\ = \frac{cos \alpha (1 + sin \alpha )}{(1 - sin {}^{2} \alpha )} \\ = \frac{\cancel{cos \alpha} + (1 + sin \alpha) }{cos {}^{\cancel{2 }}\alpha } \\ = \frac{1 + sin \alpha }{cos \alpha } \\ = RHS.$

$THANKS.$