已知0<x,y<π/2,tanx=3tany.求证x-y≤π/6

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已知0<x,y<π/2,tanx=3tany.求证x-y≤π/6已知0<x,y<π/2,tanx=3tany.求证x-y≤π/6已知0<x,y<π/2,tanx=3tany.求证x-y≤π/6tan(

已知0<x,y<π/2,tanx=3tany.求证x-y≤π/6
已知0<x,y<π/2,tanx=3tany.求证x-y≤π/6

已知0<x,y<π/2,tanx=3tany.求证x-y≤π/6
tan(x-y)=(tanx-tany)/(1+tanxtany)=2tany/(1+3tan²y)<=2tany/2√3tany=1/√3
所以x-y<=π/6