若cos(a-π/3)=1/3,a∈（π/2,π）.求cosa的值

因为cos(a-π/3)>0,a∈（π/2,π）,所以a-π/3在第一象限
cosa=cos[(a-π/3)+π/3]
=cos(a-π/3)cosπ/3-sin(a-π/3)sinπ/3
=1/3*1/2-2根号2/3×根号3/2
=（1-2根号6）/6