证明 sin(A+B)cos(A-B)=sinAcosA+sinBcosB

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证明 sin(A+B)cos(A-B)=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

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楼上证明得好