用最简单证这个恒等式sin(a+b)cos(a-b)=sinacosa+sinbcosb
1个回答

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

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