Verified answer

[tex]\displaystyle\bf\\\frac{2Sin\alpha -Sin2\alpha }{Cos\alpha -1}=\frac{2Sin\alpha -2Sin\alpha Cos\alpha }{Cos\alpha -1} =\frac{2Sin\alpha (1-Cos\alpha )}{Cos\alpha -1}=\\\\\\=-\frac{2Sin\alpha (Cos\alpha -1)}{Cos\alpha -1} =-2Sin\alpha[/tex]