三角形ABC中,a ,b c为△ABC的三边,a b c成等比数列,求(sinA+sinAcosAtanC)/(sinB+sinAcosBtanC)的范围.

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三角形ABC中,a ,b c为△ABC的三边,a b c成等比数列,求(sinA+sinAcosAtanC)/(sinB+sinAcosBtanC)的范围.

三角形ABC中,a ,b c为△ABC的三边,a b c成等比数列,求(sinA+sinAcosAtanC)/(sinB+sinAcosBtanC)的范围.
三角形ABC中,a ,b c为△ABC的三边,a b c成等比数列,
求(sinA+sinAcosAtanC)/(sinB+sinAcosBtanC)的范围.

三角形ABC中,a ,b c为△ABC的三边,a b c成等比数列,求(sinA+sinAcosAtanC)/(sinB+sinAcosBtanC)的范围.
题目应是:三角形ABC中,a ,b c为△ABC的三边,a b c成等比数列,
求(sinA+cosAtanC)/(sinB+cosBtanC)的范围
设三边的公比是q,三边为a,aq,aq^2,
原式=(sinAcosC+cosAsinC)/(sinBcosC+cosBsinC)
=sin(A+C)/sin(B+C)
=sinB/sinA
=b/a
=q
∵aq+aq^2>a,①
a+aq>aq^2②
a+aq^2>aq,③
解三个不等式可得q >(√5-1)/2
0 <q<(√5+1)/2
综述有(√5-1)/2<q<(√5+1)/2

设三边的公比是q,三边为a,aq,aq^2,
原式=(sinAcosC+cosAsinC)/(sinBcosC+cosBsinC)
=sin(A+C)/sin(B+C)
=sinB/sinA
=b/a
=q
∵aq+aq^2>a,①
a+aq>aq^2②
a+aq^2>aq,③
解三个不等式可得q >(√5-1)/2
0 <q<(√5+1)/2
综述有(√5-1)/2<q<(√5+1)/2