Question:
If $\mathrm{e}^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \infty\right) \log _{e} 2}$ 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
Correct Option: , 3
Solution:
$\mathbf{e}^{\left(\cos ^{2} x+\cos ^{4} x+\ldots \ldots \infty\right) \ln 2}=2^{\cos ^{2} x+\cos ^{4} x+\ldots \ldots \infty}$
$=2^{\cot ^{2} x}$
$t^{2}-9 t+8=0 \Rightarrow t=1,8$
$\Rightarrow 2^{\cot ^{2} x}=1,8 \Rightarrow \cot ^{2} x=0,3$
$\$ 0 \Rightarrow \frac{2 \sin x}{\sin x+\sqrt{3} \cos x}=\frac{2}{1+\sqrt{3} \cot x}=\frac{2}{4}=\frac{1}{2}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.