Let $S$ be the set of all $\alpha  \in  R$ such that the equation, $cos\,2 x + \alpha  \,sin\, x = 2\alpha  -7$ has a solution. Then $S$ is equal to

  • [JEE MAIN 2019]
  • A

    $[3, 7]$

  • B

    $R$

  • C

    $[2, 6]$

  • D

    $[1, 4]$

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  • [JEE MAIN 2024]