Evaluate the following integrals: \[ \int_{0}^{\pi / 2} \frac{1}{1+\cot x} d x \]

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The value of \( I=\int_{0}^{\pi / 2} \frac{1}{1+\cot x} d x \), is (A) \( \frac{\pi}{4} \) (B) \... The value of \( I=\int_{0}^{\pi / 2} \frac{1}{1+\cot x} d x \), is (A) \( \frac{\pi}{4} \) (B) \...