[tex]\dfrac{\sin(2\alpha)-\sin \alpha}{1+\cos(2\alpha)-\cos\alpha} = \dfrac{2\sin \alpha \cos \alpha -\sin \alpha}{1+2\cos^2 \alpha -1 - \cos \alpha} = \dfrac{\sin\alpha(2\cos \alpha-1)}{2\cos^2 \alpha - \cos \alpha} = \\ \\ = \dfrac{\sin \alpha(2\cos \alpha-1)}{\cos \alpha(2\cos \alpha -1)} = \dfrac{\sin \alpha}{\cos \alpha} = \boxed{\text{tg}\, \alpha}[/tex]
