证明2sin(a+b)cos(a-b)=sin2a+sin2b

问题描述:

证明2sin(a+b)cos(a-b)=sin2a+sin2b

2sin(a+b)cos(a-b)=2(sinacosb+sinbcosa)(cosacosb+sinasinb)=2(sinacosacos^2b+sin^2asinbcosb+sinbcosbcos^2a+sin^2bsinacosa)=2(sinacosa+sinbcosb)=sin2a+sin2b