The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is

  • A

    $2n\pi  + \frac{\pi }{3},\,n \in I$

  • B

    $n\pi  + \frac{\pi }{2},\,n \in I$

  • C

    $n\pi  + \frac{\pi }{4},\,n \in I$

  • D

    $2n\pi  - \frac{\pi }{3},\,n \in I$

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