已知α为锐角,且cos(α+π/4)=3/5,则tan α=______.

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已知α为锐角,且cos(α+π/4)=3/5,则tanα=______.已知α为锐角,且cos(α+π/4)=3/5,则tanα=______.已知α为锐角,且cos(α+π/4)=3/5,则tanα

已知α为锐角,且cos(α+π/4)=3/5,则tan α=______.
已知α为锐角,且cos(α+π/4)=3/5,则tan α=______.

已知α为锐角,且cos(α+π/4)=3/5,则tan α=______.
cos(α+π/4)=3/5
因为sin^x+cos^x=1
α为锐角,cos(α+π/4)>0
所以sin(α+π/4)>0
sin(α+π/4)=4/5
sinα=sin(α+π/4-π/4)=sin(α+π/4)cos(π/4)-cos(α+π/4)csin(π/4)=(4/5)*(根号2/2)-(3/5)*(根号2/2)=根号2/10
cosα=7*根号2/10
tan α=sinα/cosα=1/7