sinA+cosB=√3/2,(平方）
(sinA+cosB)^2=3/4
(sinA)^2+2sinAcosB+(cosB)^2=3/4.1
cosA+sinB=√2,(平方）
(cosA+sinB)^2=2
(cosA)^2+2cosAsinB+(sinB)^2=2.2
1式+2式得
2+2sinAcosB+2cosAsinB=11/4
2sinAcosB+2cosAsinB=3/4
sinAcosB+cosAsinB=3/8.3
sin(A+B)=3/8
1式-2式得
(sinA)^2+2sinAcosB+(cosB)^2-(cosA)^2-2cosAsinB-(sinB)^2=-5/8
cos2B-cos2A+2sin(A-B)=-5/8
cos2A-cos2B+2sin(B-A)=5/8
sin(A+B)sin(B-A)+sin(B-A)=5/8
[sin(A+B)+1]sin(B-A)=5/8
[3/8+1]sin(B-A)=5/8
(11/8)sin(B-A)=5/8
11sin(B-A)=5
sin(B-A)=5/11
sinBcosA-sinAcosB=5/11.4
3式+4式得
2cosAsinB=3/8+5/11=33/88+40/88=73/88
cosAsinB=73/176.5
3式-4式得
2sinAcosB=3/8-5/11=33/88-40/88=-7/88
sinAcosB=-7/176.6
6式除以5式得
tanAcotB=(-7/176)/(73/176)=-7/73