tanX,tanY是方程X²+(4M+1)X+2M=0的俩根,且M≠-1／2求sin(X+Y)／cos(X-Y)

tanX,tanY是方程X²+(4M+1)X+2M=0的俩根,且M≠-1／2求sin(X+Y)／cos(X-Y)
tanX,tanY是方程X²+(4M+1)X+2M=0的俩根,且M≠-1／2求sin(X+Y)／cos(X-Y)

tanX,tanY是方程X²+(4M+1)X+2M=0的俩根,且M≠-1／2求sin(X+Y)／cos(X-Y)
sin(X+Y)／cos(X-Y)=(tanx+tany)/(1+tanxtany)
由于tanx,tany为方程X²+(4M+1)X+2M=0的俩根
所以,tanx+tany=-(4M+1),tanxtany=2M
所以sin(X+Y)／cos(X-Y)=(tanx+tany)/(1+tanxtany)=-(4M+1)/(2M+1)

tanX,tanY是方程X²+(4M+1)X+2M=0的俩根，根据韦达定理有：
tanX+tanY = -(4M+1)
tanX tanY = 2M
M≠-1／2
sin(X+Y)／cos(X-Y) = (sinXcosY+cosXsinY)/(cosXcosY+sinxsinY)
分子分母同除以cosXcosY：
= (tanX+tanY)/(1+tanXtanY) = -(4M+1)/(1+2M)

sin(X+Y)／cos(X-Y)=(sinxcosy+cosxsiny)/(cosxcosy+sinxsiny)
分式上下同除cosxcosy得 原式=（tanx+tany）/(1+tanxtany)
因为tanx和tany是方程X²+(4M+1)X+2M=0的俩根，根据韦达定理
tanx+tany=-4m-1
tanxtany=2m
M≠-1...

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sin(X+Y)／cos(X-Y)=(sinxcosy+cosxsiny)/(cosxcosy+sinxsiny)
分式上下同除cosxcosy得 原式=（tanx+tany）/(1+tanxtany)
因为tanx和tany是方程X²+(4M+1)X+2M=0的俩根，根据韦达定理
tanx+tany=-4m-1
tanxtany=2m
M≠-1／2,所以1+2m≠0
所以原式=（-4m-1）/(1+2m)=-（4m+1）/（2m+1）

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