The number of values of x for which $sin 2 x + cos 4 x = 2$ is

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infinite

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Solution

$sin 2 x + cos 4 x = 2$
$\Rightarrow sin 2 x = 1, cos 4 x = 1$
$∴ 1 - 2 {sin}^{2} 2 x = 1$ or 1 – 2 = 1(absurd)
Thus, no solution.

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