19．已知椭圆x2a2+y2b2=1(a>b>0)\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)a2x2+b2y2=1(a>b>0)的左、右焦点分别为F1(−c,0)F_{1}(-c,0)F1(−c,0)，F2(c,0)F_{2}(c,0)F2(c,0)，若椭圆上存在一点PPP使asin∠PF1F2=csin∠PF2F1\frac{a}{\sin \angle P{F}_{1}{F}_{2}}=\frac{c}{\sin \angle P{F}_{2}{F}_{1}}sin∠PF1F2a=sin∠PF2F1c，则该椭圆的离心率的取值范围为 ___(2−1,1)({\sqrt{2}-1,1})(2−1,1)___．