JEE Math Practice Question

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:

1. A.$${{{\pi ^2}} \over 4}$$
2. B.$${{{\pi ^2}} \over 2}$$
3. C.$${\pi \over 4}$$
4. D.$${\pi \over 2}$$