x∈R:cos2x+2cos2x=2 =

x∈R:cos2x+2cos2x=2 =

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$\{x \in R : |\cos 2 x| + 2 \cos^{2} x = 2\} =$

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$\{n p + \frac{π}{3}, n \hat{I} Z\}$

$\{2 n π + \frac{π}{6}, n \in Z\}$

$\{n π \pm \frac{π}{6}, n \in Z\}$

$\{2 n π + \frac{π}{3}, n \in Z\}$

answer is C.

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Detailed Solution

$| \cos 2 x | + 2 \cos^{2} x = 2 | \cos 2 x | + 2 \cos^{2} x - 1 = 1 | \cos 2 x | + \cos 2 x = 1 2 \cos 2 x = 1 \Rightarrow \cos 2 x = \frac{1}{2} 2 x = 2 nπ \pm \frac{π}{3} x = nπ \pm \frac{π}{6}$

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$\{x \in R : |\cos 2 x| + 2 \cos^{2} x = 2\} =$