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The integral \({\int }_{0}^{\frac{\pi }{2}}\frac{1}{3+2\sin x+\cos x}dx\) is equal to: [JEE Main 2022, 29 Jul (Shift 1)]

Q1

The integral \({\int }_{0}^{\frac{\pi }{2}}\frac{1}{3+2\sin x+\cos x}dx\) is equal to:

[JEE Main 2022, 29 Jul (Shift 1)]

a

\(\tan ^{-1}(2)\)

b

\(\tan ^{-1}(2)-\frac{\pi}{4}\)

c

\(\frac{1}{2} \tan ^{-1}(2)-\frac{\pi}{8}\)

d

\(\frac{1}{2}\)

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