Simplify:

1. $$\frac{2\tan \theta }{1+{\tan }^2\theta }$$
2. $$\frac{1-{\tan }^2\theta }{1+{\tan }^2\theta }$$

In both problems, substitute $\tan \theta$ with $\frac{\sin \theta }{\cos \theta }$ and then simplify as much as possible.