Question

Please help - trig identity

Answer 1

`( \cot(x) - \csc(x) ) * ( \cos(x) + 1) \\ \\ \\ ( \: ((1)/( \tan(x) ) ) - ( (1)/( \sin(x) ) )) \: * ( \cos(x) + 1) \\ \\ \\ (( (1)/( ( \sin(x) )/( \cos(x) ) ) ) - ( (1)/( \sin(x) ) )) * ( \cos(x) + 1) \\ \\ (( ( \cos(x) )/( \sin(x) ) ) - ((1)/( \sin(x) ) )) * ( \cos(x) + 1) \\ \\ \\ ( \cos(x) - 1)/( \sin(x) ) * ( \cos(x) + 1) \\ \\ \\ ((( \cos(x) + 1) * ( \cos(x) - 1) )/( \sin(x) ) \\ \\ \\ \frac{ { \cos }^(2)(x) - 1 }{ \sin(x) } = \frac{ { - \sin }^(2) (x)}{ \sin(x) } \\ \\ = - \sin(x)`