Question

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Prove that.....

cos∅/1-tan∅ + sin∅/1-cot∅= cos∅+ sin∅

• Only correct answer will be allowed....!!!!​

Answer 1

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

Hence LHS = RHS

Answer 2

Trigonometry

refer to the attachment

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