Question

Could you please help me with this question?​

Answer 1

$HEYA \: \\ \\ GIVEN \: \: QUESTION \: \: Is \: \: \\ \\ 1 + \frac{ \cot {}^{2} ( \alpha ) }{ 1 + \csc( \alpha ) } \\ replace \: \: \csc( \alpha ) \: \: by \: \: \frac{1}{ \sin( \alpha ) } \\ and \: \\ \cot( \alpha ) \: \: by \: \: \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \\ \\ 1 + \frac{ \frac{ \cos {}^{2} ( \alpha ) }{ \sin {}^{2} ( \alpha) } }{1 + \frac{1}{ \sin( \alpha ) } } \\ \\ 1 + \frac{ \frac{ \cos {}^{2} ( \alpha ) }{ \sin( \alpha ) } }{1 + \sin( \alpha ) } \\ \\ \frac{1 + \sin( \alpha ) + \cos {}^{2} ( \alpha ) }{ \sin( \alpha ) + \sin {}^{2} ( \alpha ) } \\ \\ \frac{1 + \sin( \alpha ) + 1 - \sin {}^{2} ( \alpha ) }{ \sin( \alpha ) + \sin {}^{2} ( \alpha ) } \\ \\ \frac{1 + \sin( \alpha ) + (1 - \sin( \alpha ) ) \times (1 + \sin( \alpha ) )}{ \sin( \alpha )(1 + \sin( \alpha ) ) } \\ \\ \frac{(1 + \sin( \alpha ) )(1 + 1 - \sin( \alpha ) )}{ \sin( \alpha )(1 + \sin( \alpha )) } \\ \\ \frac{2 - \sin( \alpha ) }{ \sin( \alpha ) } \\ \\ \frac{2}{ \sin( \alpha ) } - \frac{ \sin( \alpha ) }{ \sin( \alpha ) } \\ \\ 2 \csc( \alpha ) - 1$