If $x + \frac{1}{x} = 2\cos \alpha $, then ${x^n} + \frac{1}{{{x^n}}} = $

  • A

    ${2^n}\cos \alpha $

  • B

    ${2^n}\cos n\alpha $

  • C

    $2i\,\sin \,n\,\alpha $

  • D

    $2\cos \,n\alpha $

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