已知α、β均為銳角,且cos(α+β)=sin(α-β),則tanα=______.

已知α、β均為銳角,且cos(α+β)=sin(α-β),則tanα=______.

∵cos(α+β)=sin(α-β),∴cosαcosβ-sinαsinβ=sinαcosβ-cosαsinβ,即cosβ(sinα-cosα)+sinβ(sinα-cosα)=0,∴(sinα-cosα)(cosβ+sinβ)=0,∵α、β均為銳角,∴cosβ+sinβ>0,∴sinα-cosα=0,∴tanα=1.故答案為:1