If Tan A*Tan B = 3 then what would be the value of Cos (A+B) / Cos (A-B)?

Question

If in a triangle ABC:
Cos A + Cos B + Cos C = 3/2
then what is so special about this triangle?

Answer 1

cos(A+B)/cos(A-B)
=cosAcosB-sinAsinB/cosAcosB+sinAsinB
=1-tanAtanB/1+tanAtanB
=1-3/1+3
=-2/4
=-1/2

Answer 2

The answer is -1/2.
Tan A=Sin A/Cos A
Tan B=Sin B/Cos B
Tan A*Tan B= SinASinB/CosACosB=3
SinASinB=3CosACosB
Cos(A+B)=CosACosB-SinASinB
=CosACosB - 3CosACosB
= -2CosACosB
Cos(A-B)=CosACosB + SinASinB
=CosACosB + 3CosACosB
=4CosACosB
Cos(A+B)/Cos(A-B) = -2CosACosB/4CosACosB
= -1/2.