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sinx-siny=-2/3,cosx-cosy=2/3求cos(x-y)
题目详情
sinx-siny=-2/3,cosx-cosy=2/3 求cos(x-y)
▼优质解答
答案和解析
sinx-siny=-2/3 cosx-cosy=2/3
(sinx-siny)²+(cosx-cosy)²=(-2/3)²+(2/3)²
sin²x-2sinxsiny+sin²y+cos²x-2cosxcosy+cos²y=8/9
2-2(cosxcosy+sinxsiny)=8/9
2cos(x-y)=10/9
cos(x-y)=5/9
(sinx-siny)²+(cosx-cosy)²=(-2/3)²+(2/3)²
sin²x-2sinxsiny+sin²y+cos²x-2cosxcosy+cos²y=8/9
2-2(cosxcosy+sinxsiny)=8/9
2cos(x-y)=10/9
cos(x-y)=5/9
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