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sin(x+Π/4）sin(x-Π/4）怎么化成cos2x/2
题目详情
sin(x+Π/4）sin(x-Π/4）怎么化成cos2x/2
▼优质解答
答案和解析
cos((x+π/4)+(x-π/4))=cos(x+π/4)cos(x-π/4)-sin(x+π/4)sin(x-π/4)
cos((x+π/4)-(x-π/4))=cos(x+π/4)cos(x-π/4)+sin(x+π/4)sin(x-π/4)
所以,sin(x+π/4)sin(x-π/4)=1/2(cos((x+π/4)-(x-π/4))-cos((x+π/4)+(x-π/4)))=1/2(cos(π/2)-cos2x)=-1/2cos2x
希望对你有所帮助!
cos((x+π/4)-(x-π/4))=cos(x+π/4)cos(x-π/4)+sin(x+π/4)sin(x-π/4)
所以,sin(x+π/4)sin(x-π/4)=1/2(cos((x+π/4)-(x-π/4))-cos((x+π/4)+(x-π/4)))=1/2(cos(π/2)-cos2x)=-1/2cos2x
希望对你有所帮助!
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