作业帮求证sin（a+b）cos(a–b)=sinacosb+sinbcosb
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求证sin（a+b）cos(a–b)=sinacosb+sinbcosb
求证sin（a+b）cos(a–b)=sinacosb+sinbcosb
求证sin（a+b）cos(a–b)=sinacosb+sinbcosb
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sin（a+b）cos(a–b)
=(sinacosb+cosasinb)(cosacosb+sinasinb)
=sinacosacos^2 b +sin^2 a sinbcosb +cos^2 a sinbcosb +sinacosasin^2 b
=sinacosa(1-sin^2 b) +(1-cos^2 a)sinbcosb +cos^2 a sinbcosb +...
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sin（a+b）cos(a–b)
=(sinacosb+cosasinb)(cosacosb+sinasinb)
=sinacosacos^2 b +sin^2 a sinbcosb +cos^2 a sinbcosb +sinacosasin^2 b
=sinacosa(1-sin^2 b) +(1-cos^2 a)sinbcosb +cos^2 a sinbcosb +sinacosasin^2 b
=sinacosa-sinacosasin^2 b +sinbcosb-cos^2 a sinbcosb+cos^2 a sinbcosb +sinacosasin^2 b
=sinacosa+sinbcosb
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