cos(α+π/3)=1/7,α∈（0,π/2),
则sin(α+π/3)=4√3/7,
cosα=cos[(α+π/3)-π/3]
=cos(α+π/3)cos(π/3)+sin(α+π/3)sin(π/3)
=1/14+12/14=13/14.