设cosα=负的五分之根号五，tanβ=1/3，π＜α＜3π/2,0＜β＜π/2，求α-β的值

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sinα=-2根号5/5
cosα=-根号5/厅燃5
tanβ=1/3
sinβ=根号10/10
cosβ=3根号10/10

sin(α-β)=sinαcosβ-cosαsinβ
=-6根仿蠢号50/50+根号50/50
=-5根号50/50
=-根号备伏陪2/2

α-β=5π/4

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