If 2 cos(A2)=1+sinA+1−sinA then A2 lies between n∈I

2 n π + π 4 a n d 2 n π + 3 π 4

2 n π − 3 π 4 a n d 2 n π − π 4

2 n π − π 4 a n d 2 n π + π 4

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If $2 \cos (\frac{A}{2}) = \sqrt{1 + \sin A} + \sqrt{1 - \sin A}$ then $\frac{A}{2}$ lies between $n \in I$

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$2 n π + \frac{π}{4} a n d 2 n π + \frac{3 π}{4}$

None

$2 n π - \frac{3 π}{4} a n d 2 n π - \frac{π}{4}$

$2 n π - \frac{π}{4} a n d 2 n π + \frac{π}{4}$

answer is B.

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$\sqrt{1 + \sin A} = \cos \frac{A}{2} + \sin \frac{A}{2}$

$\sqrt{1 - \sin A} = \cos \frac{A}{2} - \sin \frac{A}{2}$

$2 \cos \frac{A}{2} = \sqrt{1 + s i n A} + \sqrt{1 - \sin A}$

$∴ - \frac{π}{4} < \frac{A}{2} < \frac{π}{4}$

$2 n π - \frac{π}{4} < \frac{A}{2} < 2 n π + \frac{π}{4}$

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