Question

Trigonometry question

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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

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