上海日月光环维电子:sin(a+b)cos(a-b)=sinacosa+sinbcosb

来源:百度文库 编辑:高校问答 时间:2024/04/28 08:45:08

sin(a+b)cos(a-b)
=(sinacosb+cosasinb)(cosacosb+sinasinb)
=sinacosa(cosb)^2+(cosa)^2sinbcosb+(sina)^2sinbcosb+sinacosa(sinb)^2
=sinacosa(cosb)^2+sinacosa(sinb)^2+(cosa)^2sinbcosb+(sina)^2sinbcosb
=sinacosa+sinbcosb

sin(a+b)cos(a-b)
=(sinacosb+cosasinb)(cosacosb+sinasinb)
=sinacosa(cosb)^2+(cosa)^2sinbcosb+(sina)^2sinbcosb+sinacosa(sinb)^2
=sinacosa(cosb)^2+sinacosa(sinb)^2+(cosa)^2sinbcosb+(sina)^2sinbcosb
=sinacosa+sinbcosb