3. Given $\tan \alpha>1$, and $\sin \alpha+\cos \alpha<0$
(A) $\cos \alpha>0$
(B) $\cos \alpha<0$
(C) $\cos \alpha=0$
(D) The sign of $\cos \alpha$ is uncertain
3. B.

From $\tan \alpha>0$, we know that $\alpha$ is in the first and third quadrants.
From $\sin \alpha+\cos \alpha<0$, we know that $\alpha$ is in the second, third, and fourth quadrants.