Consider the following two statements:

P: $\sqrt { 1+ \sin{ \theta } } =a$

Q: $\sin { \cfrac { \theta }{ 2 } } +\cos { \cfrac { \theta }{ 2 } } =a$

Which of the following statements is true?

(A) P is necessary and sufficient for Q.

(B) P is necessary but not sufficient for Q.

(C) P is sufficient but not necessary for Q.

(D) P is neither necessary nor sufficient for Q.