If 1+cos x+cos ^2 x+cos ^3 x+ldots text{ to } | vedclass

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(C) The given series is an infinite geometric progression with first term $a = 1$ and common ratio $r = \cos x$.For the sum to exist,$|\cos x| < 1$.Th

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$(12n \pm 1) \frac{\pi}{6}$

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(C) The given series is an infinite geometric progression with first term $a = 1$ and common ratio $r = \cos x$.For the sum to exist,$|\cos x| The sum of an infinite geometric series is given by $S = \frac{a}{1-r}$.So,$\frac{1}{1-\cos x} = 4+2 \sqrt{3}$.$1-\cos x = \frac{1}{4+2 \sqrt{3}} = \frac{4-2 \sqrt{3}}{(4+2 \sqrt{3})(4-2 \sqrt{3})} = \frac{4-2 \sqrt{3}}{16-12} = \frac{4-2 \sqrt{3}}{4} = 1 - \frac{\sqrt{3}}{2}$.Therefore,$\cos x = \frac{\sqrt{3}}{2}$.The general solution for $\cos x = \cos 	heta$ is $x = 2n\pi \pm 	heta$.Here,$\cos x = \cos \frac{\pi}{6}$,so $x = 2n\pi \pm \frac{\pi}{6} = (12n \pm 1) \frac{\pi}{6}$.

If $1+\cos x+\cos ^2 x+\cos ^3 x+\ldots \text{ to } \infty = 4+2 \sqrt{3}$,then $x=$

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