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