∵a∈(π/2,π),b为第三象限角
∴cosa＜0,sinb＜0
∴cosa=-√(1-4/9)=-√5/3
sinb=-√(1-9/16)=-√7/4
∴cos(a+b)=cosacosb-sinasinb
=-√5/3*(-3/4)-2/3*(-√7/4)
=(2√7-3√5)/12
sin(a-b)=sinacosb-sinbcosa
=2/3*(-3/4)-(-√7/4)*(-√5/3)
=(6-√35)/12