If $\left| {\cos \,\theta \,\left\{ {\sin \theta + \sqrt {{{\sin }^2}\theta + {{\sin }^2}\alpha } } \right\}\,} \right|\, \le k,$ then the value of $k$ is

  • A

    $\sqrt {1 + {{\cos }^2}\alpha } $

  • B

    $\sqrt {1 + {{\sin }^2}\alpha } $

  • C

    $\sqrt {2 + {{\sin }^2}\alpha } $

  • D

    $\sqrt {2 + {{\cos }^2}\alpha } $

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