(sina+sinb)(cosa+cosb)=1/12,sinacosa+sinbcosb+sin(a+b)=1/12,sin(a+b)cos(a-b)+sin(a+b)=1/12；(sina+sinb)²+(cosa+cosb)²=1/16+1/9,2cos(a-b)+2=25/16*9,cos(a-b)=-263/288,代入sin(a+b)cos(a-b)+sin(a+b)=1/12,得：sin(a+b)=24/25；
(cosa+cosb)²-(sina+sinb)²=1/9-1/16,2cos(a+b)+2cos(a+b)cos(a-b)=7/16*9,得：cos(a+b)=7/25,则tan(a+b)=24/7