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 :

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 :

$\sqrt 3 $

${3 \over 2}$

2$\sqrt 3 $

${1 \over 2}$

Solution

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