已知双曲线x²/a²-y²/b²=1(a>0,b>0)的左右焦点分别为F1(-c,0)和F2(c,0),若双曲线上存在一点P,使(sin∠PF1F2)/(sin∠PF2F1)=a/c,求该双曲线的离心率的取值范围.
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![已知双曲线x²/a²-y²/b²=1(a>0,b>0)的左右焦点分别为F1(-c,0)和F2(c,0),若双曲线上存在一点P,使(sin∠PF1F2)/(sin∠PF2F1)=a/c,求该双曲线的离心率的取值范围.](/uploads/image/z/5584527-63-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%8F%8C%E6%9B%B2%E7%BA%BFx%26%23178%3B%2Fa%26%23178%3B-y%26%23178%3B%2Fb%26%23178%3B%3D1%28a%3E0%2Cb%3E0%29%E7%9A%84%E5%B7%A6%E5%8F%B3%E7%84%A6%E7%82%B9%E5%88%86%E5%88%AB%E4%B8%BAF1%28-c%2C0%29%E5%92%8CF2%28c%2C0%29%2C%E8%8B%A5%E5%8F%8C%E6%9B%B2%E7%BA%BF%E4%B8%8A%E5%AD%98%E5%9C%A8%E4%B8%80%E7%82%B9P%2C%E4%BD%BF%28sin%E2%88%A0PF1F2%29%2F%28sin%E2%88%A0PF2F1%29%3Da%2Fc%2C%E6%B1%82%E8%AF%A5%E5%8F%8C%E6%9B%B2%E7%BA%BF%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
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