sinA+sinB=1/4,cosA+cosB=1/3,求cos(A-B)的值和sin(A+B)的值
问题描述：
sinA+sinB=1/4,cosA+cosB=1/3,求cos(A-B)的值和sin(A+B)的值
答
cos(A-B)=cosAcosB+sinAsinB(sinA+sinB)^2+(cosA+cosB)^2=sin^2A+2sinAsinB+sin^2B+cos^2A+2cosAcosB+cos^B=2+2cos(A-B)=1/9+1/16cos(A-B)=-263/288(sinA+sinB)(cosA+cosB)=sinAcosA+sinBcosB+sinAcosB+cosAsinB=cos...