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(cosx)^2-(cosy)^2=1/3求sin(x+y)*sin(x-y).
题目详情
(cosx)^2-(cosy)^2=1/3求sin(x+y)*sin(x-y).
▼优质解答
答案和解析
cos²x-cos²y=1/3
sin(x+y)sin(x-y)
=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
=sin²xcos²y-cos²xsin²y
=(1-cos²x)cos²y-cos²x(1-cos²y)
=cos²y-cos²xcos²y-cos²x+cos²xcos²y
=cos²y-cos²x
=-1/3
sin(x+y)sin(x-y)
=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
=sin²xcos²y-cos²xsin²y
=(1-cos²x)cos²y-cos²x(1-cos²y)
=cos²y-cos²xcos²y-cos²x+cos²xcos²y
=cos²y-cos²x
=-1/3
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