Given \[\int\limits_{0}^{\pi /2}{\frac{dx}{1+\sin x+\cos x}=\log \,2.}\] Then the value of the definite integral \[\int\limits_{0}^{\pi /2}{\frac{\sin x}{1+\sin x+\cos x}dx}\]is equal to

\[\frac{\pi }{4}-\frac{1}{2}\log 2\]

Given \[\int\limits_{0}^{\pi /2}{\frac{dx}{1+\sin x+\cos x}=\log \,2.}

1.	Given \[\int\limits_{0}^{\pi /2}{\frac{dx}{1+\sin x+\cos x}=\log \,2.}\] Then the value of the definite integral \[\int\limits_{0}^{\pi /2}{\frac{\sin x}{1+\sin x+\cos x}dx}\]is equal to
A.	\[\frac{1}{2}\log 2\]
B.	\[\frac{\pi }{2}-\log 2\]
C.	\[\frac{\pi }{4}-\frac{1}{2}\log 2\]
D.	\[\frac{\pi }{2}+\log 2\]
Answer» D. \[\frac{\pi }{2}+\log 2\]

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Given \[\int\limits_{0}^{\pi /2}{\frac{dx}{1+\sin x+\cos x}=\log \,2.}\] Then the value of the definite integral \[\int\limits_{0}^{\pi /2}{\frac{\sin x}{1+\sin x+\cos x}dx}\]is equal to

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