sinx+siny=sin((x+y)/2+(x-y)/2)+sin((x+y)/2-(x-y)/2)=1/3
cosx+cosy=cos((x+y)/2+(x-y)/2)+cos((x+y)/2-(x-y)/2)=1/4
根據(jù)三角函數(shù)公式化簡(jiǎn)得
2cos[(x-y)/2]sin[(x+y)/2]=1/3
2cos[(x+y)/2]cos[(x-y)/2]=1/4
tan[(x+y)/2]=4/3
cos[(x+y)/2]=+-3/5
sin[(x+y)/2]=+-4/5(由于tan>0,sin,cos 必須同號(hào)）
sin(x+y)=2(12)/25 =24/25 （cos[(x+y)/2],sin[(x+y)/2]同號(hào),乘積為正）
cos(x+y)=2(cos[(x+y)/2])^2-1=-7/25
tan(x+y)=sin(x+y)/cos(x+y)=-24/7