(a+b)/c=5/4,正弦定理：(sinA+sinB)/sinC=5/4,
[2sin((A+B)/2)cos((A-B) /2)]/[2sin((A+B)/2)cos((A+B)/2)] =5/4,
约掉2sin((A+B)/2)并展开解得cos(A/2)cos(B/2)=9 sin(A/2)sin(B/2),tan(A/2)tan(B/2)=1/9.