Answer:
[tex]( \cot(x) - \csc(x) ) \times ( \cos(x) + 1) \\ \\ \\ ( \: (\frac{1}{ \tan(x) } ) - ( \frac{1}{ \sin(x) } )) \: \times ( \cos(x) + 1) \\ \\ \\ (( \frac{1}{ \frac{ \sin(x) }{ \cos(x) } } ) - ( \frac{1}{ \sin(x) } )) \times ( \cos(x) + 1) \\ \\ (( \frac{ \cos(x) }{ \sin(x) } ) - (\frac{1}{ \sin(x) } )) \times ( \cos(x) + 1) \\ \\ \\ \frac{ \cos(x) - 1}{ \sin(x) } \times ( \cos(x) + 1) \\ \\ \\ \frac{(( \cos(x) + 1) \times ( \cos(x) - 1) }{ \sin(x) } \\ \\ \\ \frac{ { \cos }^{2}(x) - 1 }{ \sin(x) } = \frac{ { - \sin }^{2} (x)}{ \sin(x) } \\ \\ = - \sin(x) [/tex]
