If \( e^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \infty\right) \log _{e} 2} \) satisfie...

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If \( e^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \infty\right) \log _{e} 2} \) satisfies the equation
\( \mathrm{P} \) \( t^{2}-9 t+8=0 \), then the value of \( \frac{2 \sin x}{\sin x+\sqrt{3} \cos x} \)

W \( \left(0x\frac{\pi}{2}\right) \) is
[JEE Main-2021 (February)]
(a) \( \frac{3}{2} \)
(b) \( 2 \sqrt{3} \)
(c) \( \frac{1}{2} \)
(d) \( \sqrt{3} \)
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