热心网友
已知sina+sinb=1,cosa+cosb=0求cos2a+cos2b的值由sina+sinb=1 ……（1）cosa+cosb=0 ……（2）(2)^2+(1)^2 得2cosacosb+2sinasinb=-1即cos(a-b)=-1/2(2)^2-(1)^2 得cos2a+cos2b+2cosacosb-2sinasinb=-1即cos(a+b)=[1-(cos2a+cos2b)]/2又cos2a+cos2b=2cos(a+b)cos(a-b)=2×(-1/2)[1-(cos2a+cos2b)]/2即cos2a+cos2b=-[1-(cos2a+cos2b)]/2解得cos2a+cos2b=-1