20.78 Let $A B C D$ be a cyclic quadrilateral. Now, four relations are given:
(1) $\sin A=\sin C$;
(2) $\sin A+\sin C=0$;
(3) $\cos B+\cos D=0$;
(4) $\cos B=\cos D$.

The number of relations that always hold is
(A) one.
(B) two.
(C) three.
(D) four.
(China Junior High School Mathematics League, 1985)
[Solution] Since $A B C D$ is a cyclic quadrilateral, $\angle C=180^{\circ}-\angle A$, and $\angle A$, $\angle C$ cannot be 0 or $180^{\circ}$, therefore (1) always holds; (2) never holds.

Similarly, since $\angle D=180^{\circ}-\angle B$, (3) always holds; (4) only holds when $\angle B=\angle D=90^{\circ}$.
In summary, only two relations always hold.
Therefore, the answer is $(B)$.