ДОКАЖИТЕ ТОЖДЕСТВО: [latex] \frac{sin2a-sina}{1-cosa+cos2a}=tga [/latex]

[latex]\frac{\sin2 \alpha -\sin \alpha }{1-\cos \alpha +\cos2 \alpha }=\frac{2\sin \alpha \cos \alpha -\sin \alpha }{\cos^2 \alpha +\sin^2 \alpha -\cos \alpha +\cos^2 \alpha -\sin^2 \alpha }=\frac{\sin \alpha (2\cos \alpha -1)}{2\cos^2 \alpha -\cos \alpha }=\\\\=\frac{\sin \alpha (2\cos \alpha -1)}{\cos \alpha (2\cos\alpha -1)}=\frac{\sin \alpha }{\cos \alpha }=tg \alpha .[/latex]