$\begin{array}{l}m) \, M = \dfrac{1 + \cos\alpha - \sin\alpha}{1 - \cos\alpha - \sin\alpha}\\ = \dfrac{(1 + \cos\alpha - \sin\alpha)(1 + \cos\alpha + \sin\alpha)}{(1 - \cos\alpha - \sin\alpha)(1 + \cos\alpha + \sin\alpha)}\\ = \dfrac{(1 + \cos\alpha)^2 - \sin^2\alpha}{1 - (\cos\alpha + \sin\alpha)^2}\\ = \dfrac{1 + 2\cos\alpha + \cos^2\alpha - \sin^2\alpha}{1 - (1 +2\sin\alpha\cos\alpha)}\\ =\dfrac{2\cos\alpha + 2\cos^2\alpha}{-2\sin\alpha\cos\alpha}\\ = - \dfrac{\cos\alpha +1}{\sin\alpha}\end{array}$
