The value of $\int\limits_0^\pi {{{{e^{\cos x}}\sin x} \over {(1 + {{\cos }^2}x)({e^{\cos x}} + {e^{ - \cos x}})}}dx} $ is equal to:

Question

${{{\pi ^2}} \over 4}$

${{{\pi ^2}} \over 2}$

${\pi \over 4}$

${\pi \over 2}$

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