设0小于a小于90°小于b小于180°,且sin（a+b)=5/13,cosa/2=2根号5/5

tana=2(tana/2)/[1-(tana/2)^2]
=2*1/2/[1-1/4]
=1/(3/4)
=4/3
sina=4/5,cosa=3/5
sin(a+b)
=sinacosb+cosasinb
=4/5cosb+3/5sinb
=4/5cosb+3/5√(1-cos^2 b)
5/13=4/5cosb+3/5√(1-cos^2 b)
5/13-4/5cosb=3/5√(1-cos^2 b)
25/169+16/25cos^2b-8/13cosb=9/25(1-cos^2 b)
25/169+cos^2b-8/13cosb-9/25=0
cos^2b-8/13cosb-896/4225=0
cos^2b-8/13cosb+16/169-16/169-896/4225=0
(cosb-4/13)^2-1296/4225=0
(cosb-4/13-36/65)(cosb-4/13+36/65)=0
(cosb-20/65-36/65)(cosb-20/65+36/65)=0
(cosb-56/65)(cosb+16/65)=0
cosb=56/65或cosb=-16/65
因为90°

tan(a-b)/2=(tana/2-tanb/2)/(1+tana/2*tanb/2)=(1/2-9/7)/(1+1/2*9/7)=(7/14-18/14)/(1+9/14)=(-11/14)/(23/14)=-11/23