434. 

$$
\frac{1-\cos 2 \alpha+\sin 2 \alpha}{1+\cos 2 \alpha+\sin 2 \alpha}
$$
Solution. Applying formulas (13), (12), and (9) sequentially, factoring out the common factor, and transforming, we find

$\frac{(1-\cos 2 \alpha)+\sin 2 \alpha}{(1+\cos 2 \alpha)+\sin 2 \alpha}=\frac{2 \sin ^{2} \alpha+2 \sin \alpha \cos \alpha}{2 \cos ^{2} \alpha+2 \sin \alpha \cos \alpha}=\frac{2 \sin \alpha(\sin \alpha+\cos \alpha)}{2 \cos \alpha(\cos \alpha+\sin \alpha)}=\frac{\sin \alpha}{\cos \alpha}=\operatorname{tg} \alpha$.