If $\tan \theta + \sin \theta = m$ and $\tan \theta - \sin \theta = n,$ then

  • [IIT 1970]
  • A

    ${m^2} - {n^2} = 4\,mn$

  • B

    ${m^2} + {n^2} = 4\,mn$

  • C

    ${m^2} - {n^2} = {m^2} + {n^2}$

  • D

    ${m^2} - {n^2} = 4\sqrt {mn} $

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