If $\cos \,\alpha  + \cos \,\beta  = \frac{3}{2}$ and $\sin \,\alpha  + \sin \,\beta  = \frac{1}{2}$ and $\theta $ is the the arithmetic mean of $\alpha $ and $\beta $ , then $\sin \,2\theta  + \cos \,2\theta $ is equal to 

  • [JEE MAIN 2015]
  • A

    $\frac{3}{5}$

  • B

    $\frac{7}{5}$

  • C

    $\frac{4}{5}$

  • D

    $\frac{8}{5}$

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