What am I doing wrong? (Trigonometric Identity) $$\frac { \cos\theta  }{ 1-\sin\theta  } =\frac { \sin\theta -\csc\theta  }{ \cos\theta -\cot\theta  } $$
Steps I took:
$$\frac { \sin\theta -\frac { 1 }{ \sin\theta  }  }{ \cos\theta -\frac { \cos\theta  }{ \sin\theta  }  } $$
$$\frac { \frac { \sin^{ 2 }\theta -1 }{ \sin\theta  }  }{ \frac { \sin\theta \cos\theta -\cos\theta  }{\sin\theta  }  } $$
$$\frac { \sin^{ 2 }\theta -1 }{ \sin\theta  } \cdot \frac { \sin\theta  }{ \sin\theta \cos\theta -\cos\theta  } $$
$$\frac { (\sin^{ 2 }\theta -1) }{ (\cos\theta )(\sin\theta -1) } $$
Now where do I go from here? As far as I can tell, $\sin^{ 2 }\theta -1=-\cos^2\theta $ 
so this makes no sense to me.

$\dfrac{\sin^2\theta-1}{\cos \theta(\sin\theta-1)}=\dfrac{-\cos^2\theta}{\cos \theta(\sin\theta-1)}=\dfrac{-\cos\theta}{\sin\theta-1}=\dfrac{\cos\theta}{1-\sin\theta}$
