Question

prove that the problem​

Answer 1

LHS

$\frac{ \sin( \alpha ) }{1 + \cos( \alpha ) } + \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } \\ \\⇒ \frac{ \sin( \alpha ) + (1 + \cos( \alpha) ) {}^{2} }{(1 + \cos( \alpha) ) \sin( \alpha ) } \\ \\⇒ \frac{2 + 2 \cos( \alpha ) }{(1 + \cos( \alpha )) \sin( \alpha ) } \\ \\ ⇒ \frac{2(1 + \cos( \alpha )) }{(1 + \cos( \alpha )) \sin( \alpha ) } \\ \\ ⇒ \frac{2}{ \sin( \alpha ) } \\ \\ ⇒ 2 \csc( \alpha )$

RHS

Hence proved

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