Necessary /Sufficient - Trigo

Geometry Level 4

Consider the following two statements:

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

Q: sinθ2+cosθ2=a\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.

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