The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is

  • [IIT 2015]
  • A

    $5$

  • B

    $6$

  • C

    $7$

  • D

    $8$

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  • [JEE MAIN 2022]