If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$

  • A

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

  • B

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

  • C

    $4\pi (2n + 1)$

  • D

    None of these

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  • [IIT 2010]