$\smallint \,\,\frac{{dx}}{{1 - \cos \,\,x - \sin \,\,x}}$ is equal to

$\log \,\,\left| {1 - \tan \,\,\frac{x}{2}} \right| + c$

$\log \,\,\left| {1 + \tan \,\,\frac{x}{2}} \right| + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{{dx}}{{1 - \cos \,\,x - \sin \,\,x}}

is equal to

View answer and explanation

Correct option: C

\log \,\,\left| {1 - \cot \,\,\frac{x}{2}} \right| + c

Option C is correct because the integral simplifies to

\log \,\,\left| {1 - \cot \,\,\frac{x}{2}} \right| + c

after using trigonometric identities and substitution.