7 . 14 Condition A: $\sqrt{1+\sin \theta}=a$. Condition B: $\sin \frac{\theta}{2}+\cos \frac{\theta}{2}=a$. Then
(A) A is a necessary and sufficient condition for B.
(B) A is a necessary condition for B.
(C) A is a sufficient condition for B.
(D) A is neither a necessary condition nor a sufficient condition for B.
(China High School Mathematics Competition, 1981)
［Solution] In condition A, $a \geqslant 0$, while in condition B, $a$ can take negative values, so A does not imply B; and B does not imply A either.
Therefore, the answer is $(D)$.