JEE Math Practice Question

If $${e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}$$ satisfies the equation t2 - 9t + 8 = 0, then the value of $${{2\sin x} \over {\sin x + \sqrt 3 \cos x}}\left( {0 < x < {\pi \over 2}} \right)$$ is :

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