已知$$-\frac{ \pi }{2} ~\textless{} ~\alpha ~~\textless{} ~\frac{ \pi }{2}$$，$$2\tan \beta =\tan 2\alpha $$．$$\tan \left( \beta -\alpha \right)=-2\sqrt{2}$$，则$$\cos \alpha =$$（~ ）．
选项为:A:$$\frac{\sqrt{3}}{2}$$  B:$$\frac{\sqrt{2}}{2}$$  C:$$\frac{\sqrt{3}}{3}$$  D:$$\frac{\sqrt{2}}{3}$$  请回答其中一个选项.