$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r - 1}}}}{{\cos \,{2^r}}}} $ is equal to

  • A

    $tan\,2^{99} -tan\,1$

  • B

    $tan\,2^{100}$

  • C

    $tan\,2^{100} -tan\,1$

  • D

    none of these

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