Common roots of the equations $2{\sin ^2}x + {\sin ^2}2x = 2$ and $\sin 2x + \cos 2x = \tan x,$ are

  • A

    $x = (2n - 1)\frac{\pi }{2}$

  • B

    $x = (2n + 1)\frac{\pi }{4}$

  • C

    $x = (2n + 1)\frac{\pi }{3}$

  • D

    None of these

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