sin(a+b)*cos(a-b)
=(sinacosb+cosbsina)(cosacosb+sinasinb)
=sinacosbcosacosb+sinacosbsinasinb+cosbsinacosacosb+cosbsinasinasinb
=sinacosacos^2b+sin^2asinbcosb+sinacosacos^2b+sin^2asinbcosb
=(sinacosacos^2b+sinacosacos^2b)+(sin^2asinbcosb+sin^2asinbcosb)
=2sinacosacos^2b+2sin^2asinbcosb
=2sinacosb(cosacosb+sinasinb)=2sinacosbcos(a-b)
追问为什么=(sinacosb+cosbsina)(cosacosb+sinasinb)??
本回答被网友采纳