Question

Show that:-
$\frac{1 + cos \alpha }{ {sin}^{2} \: \alpha } = \frac{1}{1 - cos \: \alpha }$
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Answer 1

Answer:

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