3. $\angle A 、 \angle B 、 \angle C$ are the interior angles of $\triangle A B C$.

Proposition 甲: $\angle A=\angle C$;
Proposition 乙: $\cos \frac{B}{2}=\sin C$.
Then 甲 is the $\qquad$ condition of 乙.
3. Sufficient but not necessary.

When $\angle A=\angle C$, $\frac{\angle B}{2}+\angle C=\frac{\pi}{2}$.
Thus, $\cos \frac{B}{2}=\sin C$;
When $\angle A=\frac{3 \pi}{8}, \angle B=\frac{\pi}{12}, \angle C=\frac{13 \pi}{24}$, $\cos \frac{B}{2}=\sin C$, but $\angle A \neq \angle C$.