The number of integral values of $k$, for which the equation $7\cos x + 5\sin x = 2k + 1$ has a solution, is

  • [IIT 2002]
  • A

    $4$

  • B

    $8$

  • C

    $10$

  • D

    $12$

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Common roots of the equations $2{\sin ^2}x + {\sin ^2}2x = 2$ and $\sin 2x + \cos 2x = \tan x,$ are