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

$a = \frac{{5\,\pi }}{4},\;\,b \in R$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

, then

View answer and explanation

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 integrating the given expression using trigonometric identities and comparing it with the target form.