A) \[2\]
B) \[-2\]
C) \[\frac{1}{2}\]
D) \[-\frac{1}{2}\]
Correct Answer: A
Solution :
\[\int_{\pi /4}^{3\pi /4}{\frac{1}{1+\cos x}}dx=\int_{\pi /4}^{3\pi /4}{\frac{1-\cos x}{{{\sin }^{2}}x}}dx\] \[=\int_{\pi /4}^{3\pi /4}{(\text{cose}{{\text{c}}^{2}}x-\cot x\,\,\text{cosec}x)\,dx}\] \[=[-\cot x+\text{cosec}x]_{\pi /4}^{3\pi /4}\] \[=(1+\sqrt{2})-(-1+\sqrt{2})\] \[=2\]
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