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Gaokao Math Practice Question

已知 $\alpha, \beta \in R$, 则“存在 $k \in Z$ 使得 $\alpha=k \pi+(-1)^{k} \beta$ ”是“ $\sin \alpha=\sin \beta$ ”的 ($\quad$).

  1. A.充分而不必要条件
  2. B.必要而不充分条件
  3. C.充分必要条件
  4. D.既不充分也不必要条件

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