【高中数学】已知cos(x+y)=1/3,cos(x-y)=2/3,且0

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【高中数学】已知cos(x+y)=1/3,cos(x-y)=2/3,且0

【高中数学】已知cos(x+y)=1/3,cos(x-y)=2/3,且0
【高中数学】已知cos(x+y)=1/3,cos(x-y)=2/3,且0

【高中数学】已知cos(x+y)=1/3,cos(x-y)=2/3,且0
0π/3-π/3所以sin(x+y)=2根号2/3,sin(x-y)=-根号5/3
所以
cos2x
=cos(x+x+y-y)
=cos(x+y+x-y)
=cos(x+y)cos(x-y)-sin(x+y)sin(x-y)
=2/9+2根号10/9
=2/9(1-根号10)

π/30
因为cos(x+y)>0 所以 π/3-π/2cos2x=cos(x+y+x-y)
=cos(x+y)cos(x-y)-sin(x+y)sin(x-y)
=1/3*2/3-(2/3*根号2)*(-根号5/3)
=(2+2根号10)/9sin(x-y) ...

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π/30
因为cos(x+y)>0 所以 π/3-π/2cos2x=cos(x+y+x-y)
=cos(x+y)cos(x-y)-sin(x+y)sin(x-y)
=1/3*2/3-(2/3*根号2)*(-根号5/3)
=(2+2根号10)/9

收起

cos2x=cos[(x+y)+(x-y)]=