The number of real numbers $\lambda$ for which the equality $\frac{\sin (\lambda \alpha) \quad \cos (\lambda \alpha)}{\sin \alpha}=\lambda-1$,holds for all real $\alpha$ which are not integral multiples of $\pi / 2$ is

  • [KVPY 2015]
  • A

    $1$

  • B

    $2$

  • C

    $3$

  • D

    infinite

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