$cos (\alpha \,-\,\beta ) = 1$ and $cos (\alpha  +\beta ) = 1/e$ , where $\alpha , \beta \in [-\pi , \pi ]$ . Number of pairs of $(\alpha ,\beta )$ which satisfy both the equations is

  • A

    $0$

  • B

    $1$

  • C

    $2$

  • D

    $4$

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