Using the formula $$\tan\frac{x}{2}=\frac{1-\cos x}{\sin x}$$, find the value of $$\tan 22.5^{0}$$.

A

$$\sqrt{2}-1$$

B

$$\sqrt{2}+1$$

C

$$\frac{\sqrt{3}+\sqrt{2}}{2}$$

D

$$\frac{\sqrt{3}-\sqrt{2}}{2}$$