f(x)=cos²x -√3sinxcosx +1=(1+cos2x)/2-(√3/2)sin2x +1=sin(π/6 - 2x)＋3/2因为,f(a)=5/6所以,sin(π/6 -2a)＋3/2=5/6即,sin(2a-π/6)＝2/3因为,π/3≤a≤2π/3所以,π/2≤2a-π/6≤7π/6所以,cos(2a-π/6)...