Алгебра.Доказать тождество

$\sf\displaystyle \frac{1-\cos2\alpha+\sin2\alpha}{1+\cos2\alpha+\sin2\alpha}=tg\alpha\\\\ \frac{1-(1-2\sin^2\alpha)+2\cos\alpha\sin\alpha}{1+2\cos^2\alpha-1+2\cos\alpha\sin\alpha}=\frac{\sin\alpha}{\cos\alpha}\\\\ \frac{2\sin^2\alpha+2\cos\alpha\sin\alpha}{2\cos^2\alpha+2\cos\alpha\sin\alpha}=\frac{\sin\alpha}{\cos\alpha}\\\\ \frac{\sin\alpha(2\sin\alpha+2\cos\alpha)}{\cos\alpha(2\sin\alpha+2\cos\alpha)}=\frac{\sin\alpha}{\cos\alpha}\\\\ \frac{\sin\alpha}{\cos\alpha}=\frac{\sin\alpha}{\cos\alpha}$

Ч.Т.Д.