3. The following 4 propositions are given:
(1) In $\triangle A B C$, $\sin A+\sin B-\sin C$ is always positive;
(2) In $\triangle A B C$, $\cos A+\cos B+\cos C$ is always positive;
(3) In $\triangle A B C$, $\cot A+\cot B+\cot C$ is always positive;
(4) In a non-right $\triangle A B C$, $\tan A+\tan B+\tan C$ is always positive.
Among them, the correct propositions are ( ) in number.
(A) 4
(B) 3
(C) 2
(D) 1
3. B.
(1) Correct. By the Law of Sines, we have
$$
\sin A+\sin B-\sin C=\frac{1}{2 R}(a+b-c)>0 \text {. }
$$
(2) Correct. When $\triangle A B C$ is an acute or right triangle, the algebraic expression is clearly positive. When $\triangle A B C$ is an obtuse triangle, assume without loss of generality that $\angle C$ is the obtuse angle, then $0\cos (A+B)$, which means $\cos A+\cos C>0$. Since $\cos B > 0$, it follows that $\cos A+\cos B+\cos C>0$.
(3) Correct. Same as (2).
(4) Incorrect. By
$$
\tan A+\tan B+\tan C=\tan A \cdot \tan B \cdot \tan C \text {, }
$$

we know that when $\triangle A B C$ is an obtuse triangle, its value is negative.