证明2sin(a+b)cos(a-b)=sin2a+sin2b

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证明2sin(a+b)cos(a-b)=sin2a+sin2b证明2sin(a+b)cos(a-b)=sin2a+sin2b证明2sin(a+b)cos(a-b)=sin2a+sin2b2sin(a+

证明2sin(a+b)cos(a-b)=sin2a+sin2b
证明2sin(a+b)cos(a-b)=sin2a+sin2b

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

2sin(a+b)cos(a-b)=2(sinacosb+sinbcosa)(cosacosb-sinasinb)
=2(sinacosacosbcosb+cosacosasinbcosb-sinasinasinbcosb-sinbsinbsinacosa)
=2(cos2b*sin2a/2+cos2a*sin2b/2)
=sin(2a+2b)不等于sin2a+sin2b
所以题目错了

由右向左证,很简单的和差化积