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
根据三角函数公式化简得
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 必须同号）
sin(x+y)=2(12)/25 =24/25 （cos[(x+y)/2],sin[(x+y)/2]同号,乘积为正）
cos(x+y)=2(cos[(x+y)/2])^2-1=-7/25
tan(x+y)=sin(x+y)/cos(x+y)=-24/7