If $\left| {\,\begin{array}{*{20}{c}}{\cos (A + B)}&{ - \sin (A + B)}&{\cos 2B}\\{\sin A}&{\cos A}&{\sin B}\\{ - \cos A}&{\sin A}&{\cos B}\end{array}\,} \right| = 0$, then $B =$

  • A

    $(2n + 1)\frac{\pi }{2}$

  • B

    $n\pi $

  • C

    $(2n + 1)\frac{\pi }{2}$

  • D

    $2n\pi $

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