If $\operatorname{cosec}^2(\alpha+\beta)-\sin ^2(\beta-\alpha)+\sin ^2(2 \alpha-\beta)=\cos ^2(\alpha-\beta)$ where $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, then $\sin (\alpha-\beta)$ is equal to

  • [KVPY 2009]
  • A

    $-\frac{1}{2}$

  • B

    $\frac{1}{2}$

  • C

    $\frac{-\sqrt{3}}{2}$

  • D

    $\frac{\sqrt{3}}{2}$

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