1>tanAtanB>0
1>(sinAsinB)/(cosAocsB)>0
∵sinAsinB>0,∴cosAcosB>0
∴sinAsinBcosAcosB-sinAsinB>0
===>cos(A+B)>0===>cos(π-C)>0===>cosC
1>tanAtanB>0
1>(sinAsinB)/(cosAocsB)>0
∵sinAsinB>0,∴cosAcosB>0
∴sinAsinBcosAcosB-sinAsinB>0
===>cos(A+B)>0===>cos(π-C)>0===>cosC