sina+sinb=2sin(a+b)/2cos(a-b)/2.(1)
cosa+cosb=2cos(a+b)/2cos(a-b)/2.(2)
(1)式/(2)式得:
tan[(a+b)/2] =(sina+sinb)/(cosa+cosb)=2
sin(a+b)=(2tan(a+b)/2)/(1+tan^2((a+b)/2))=2*2/(1+2^2)=4/5,
cos(a+b)=(1-tan^2(a+b)/2)/(1+tan^2(a+b)/2)=(1-2^2)/(1+2^2)=-3/5
所以tan(a+b)=sin(a+b)/cos(a+b)=(4/5)/(-3/5)=-4/3