If $\cos (\alpha - \beta ) = 1$ and $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, then total number of ordered pair of $(\alpha ,\beta )$ is

  • [IIT 2005]
  • A

    $0$

  • B

    $1$

  • C

    $2$

  • D

    $4$

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