ＳＩＮＡ加ＳＩＮＢ＝１，ＣＯＳＡ加ＣＯＳＢ＝０，求ＣＯＳ２Ａ加ＣＯＳ２Ｂ
热心网友
sinA+sinB=2sin0.5(A+B)cos0.5(A-B)=1cosA+cosB=2cos0.5(A+B)cos(0.5(A-B)=0cos0.5(A-B)≠0,cos0.5(A+B)=0,sin２0.5(A+B)=1，cos２0.5(A-B)=1/4cos2A+cos2B=2cos(A+B)cos(A-B)=2(1-2sin２0.5(A+B))(2cos２0.5(A-B)-1)=2*(-1)*(-1/2)=1或者(sinA+sinB)^2+(cosA+cosB)^2=2+2cos(A-B)=1cos(A-B)=-1/2(cosA+cosB)^2-(sinA+sinB)^2=cos2A+cos2B+2cos(A+B)=-1即2cos(A+B)cos(A-B)+2cos(A+B)=-1cos(A+B)=-1cos2A+cos2B=1
热心网友
因为sina+sinb=1,cosa+cosb=0,所以sina=1-sinb,cosa=-cosb又因为(sina)^2+(cosa)^2=1,所以(1-sinb)^2+(cosb)^2=1,而(sinb)^2+(cosb)^2=1所以(1-sinb)^2=(sinb)^2,所以1-2sinb=0,所以sinb=1/2,同理,因为(sinb)^2+(cosb)^2=1,所以(1-sina)^2+cosa^2=1,而(sina)^2+(cosa)^2=1所以(1-sina)^2=(sina)^2,所以1-2sina=0,所以sina=1/2所以cos2a+cos2b=1-2(sina)^2+1-2(sinb)^2=1-1/4+1-1/4=3/2