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求证:sin(x-y)sin(x+y)/sin²xcos²y=1-cot²xtan

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/11/07 22:43:26
求证:sin(x-y)sin(x+y)/sin²xcos²y=1-cot²xtan²y
sin(x-y)=sinxcosy-cosxsiny,
sin(x+y)=sinxcosy+cosxsiny
sin(x-y)sin(x+y)=sin²xcos²y-cos²xsin²y
sin(x-y)sin(x+y)/sin²xcos²y=(sin²xcos²y-cos²xsin²y)/sin²xcos²y
=1-cot²xtan²y
再问: (sin²xcos²y-cos²xsin²y)/sin²xcos²y =1-cot²xtan²y 这步怎么得到的?
再答: 把括号的每一项都除分母就行了
再问: 哦,谢谢了