神马作文网化简sin^2a+sin^2b+2sinasinbcos（a+b）
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/06 03:04:18
化简sin^2a+sin^2b+2sinasinbcos（a+b）
sin^2a+sin^2b+2sinasinbcos（a+b）
=sin^2a+sin^2b+2sinasinb(cosacosb-sinasinb)
=(sin^2a-sin^2asin^2b)+(sin^2b-sin^2asin^2b)+2sinasinbcosacosb
=sin^2acos^2b+sin^2bcos^2a+2sinasinbcosacosb
=(sinacosb+sinbcosa)^2
=[sin(a+b)]^2
=sin^2a+sin^2b+2sinasinb(cosacosb-sinasinb)
=(sin^2a-sin^2asin^2b)+(sin^2b-sin^2asin^2b)+2sinasinbcosacosb
=sin^2acos^2b+sin^2bcos^2a+2sinasinbcosacosb
=(sinacosb+sinbcosa)^2
=[sin(a+b)]^2
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