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

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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 $ t^{2}-9 t+8=0 $, then the value of $ \frac{2 \sin x}{\sin x+\sqrt{3} \cos x} $ $ \left(0<x<\frac{\pi}{2}\right) $ is [JEE Main 2021, 24 Feb (Shift 1)]

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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 \( t^{2}-…

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