If \[\int_{{}}^{{}}{\frac{{{e}^{x}}(1+\sin x)dx}{1+\cos x}={{e}^{x}}f(x)+c}\], then \[f(x)=\] [RPET 1997; Karnataka CET 2003, 05; Orissa JEE 2004]

If \[\int_{{}}^{{}}{\frac{{{e}^{x}}(1+\sin x)dx}{1+\cos x}={{e}^{x}}f(

1.	If \[\int_{{}}^{{}}{\frac{{{e}^{x}}(1+\sin x)dx}{1+\cos x}={{e}^{x}}f(x)+c}\], then \[f(x)=\] [RPET 1997; Karnataka CET 2003, 05; Orissa JEE 2004]
A.	\[\sin \frac{x}{2}\]
B.	\[\cos \frac{x}{2}\]
C.	\[\tan \frac{x}{2}\]
D.	\[\log \frac{x}{2}\]
Answer» D. \[\log \frac{x}{2}\]

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If \[\int_{{}}^{{}}{\frac{{{e}^{x}}(1+\sin x)dx}{1+\cos x}={{e}^{x}}f(x)+c}\], then \[f(x)=\] [RPET 1997; Karnataka CET 2003, 05; Orissa JEE 2004]

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