If \( \int \frac{d x}{1+\sin x}=\tan \left(\frac{x}{2}+a\right)+c \), then \( a \) is equal to....

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If \( \int \frac{d x}{1+\sin x}=\tan \left(\frac{x}{2}+a\right)+c \), then \( a \) is equal to
\( \mathrm{P} \)
(1) \( \frac{\pi}{4} \)
(2) \( \frac{\pi}{2} \)
(3) \( -\frac{\pi}{2} \)
(4) \( -\frac{\pi}{4} \)



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