sin²A+cosA=5/4,1-cos²A+cosA=5/4,解得cosA=1/2
b+c=√3a,即sinB+sinC=√3sinA=3/2=2sin((B+C)/2)cos((B-C)/2)
sin((B+C)/2)=sin60=√3/2
∴cos((B-C)/2)=√3/2