If $\tan \theta + \sec \theta = {e^x},$ then $\cos \theta $ equals

  • A

    $\frac{{({e^x} + {e^{ - x}})}}{2}$

  • B

    $\frac{2}{{({e^x} + {e^{ - x}})}}$

  • C

    $\frac{{({e^x} - {e^{ - x}})}}{2}$

  • D

    $\frac{{({e^x} - {e^{ - x}})}}{{({e^x} + {e^{ - x}})}}$

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