If $\int \frac{1}{1+\sin x} d x=\tan \left(\frac{x}{2}+a\right)+b$, then

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{1}{1+\sin x} d x=\tan \left(\frac{x}{2}+a\right)+b

, then

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Correct option: A

a=-\frac{\pi}{4}, b \in R

Option A (

a=-\frac{\pi}{4}, b \in R

) is correct because it is obtained by manipulating the integral using trigonometric identities and comparing the result with the given form.

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