Simplify: $$\frac{\tan A}{(1 + \tan^2 A)^2} + \frac{\cot A}{(1 + \cot^2 A)^2}$$

A

$$(\sin A + \cos A)^2$$

B

$$\sin A - \cos A$$

C

$$\sin A  \cos A$$

D

$$2\sin A  \cos A$$