若 $\sin (\alpha+\beta)+\cos (\alpha+\beta)=2 \sqrt{2} \cos \left(\alpha+\frac{\pi}{4}\right) \sin \beta$, 则
A. $\tan (\alpha-\beta)=1$
B. $\tan (\alpha+\beta)=1$
C. $\tan (\alpha-\beta)=-1$
D. $\tan (\alpha+\beta)=-1$