已知:sina+sinb=0.5,cosa+cosb=0.5求 sin(a+b)的值
热心网友
由已知:sina+sinb=0.5(1),cosa+cosb=0.5(2) (1)平方+(2)平方:2+2(sinasinb+cosacosb)=1/22cos(a-b)=-3/2,cos(a-b)=-3/4 (*)(2)平方-(1)平方;cos2a+cos2b+2cos(a+b)=0和差化积2cos(a+b)cos(a-b)+2cos(a+b)=0cos(a+b)[cos(a-b)+1]=0,将(*)代入cos(a+b)[-3/4+1]=0,得cos(a+b)=0,故sin(a+b)=1