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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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
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

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
sinα=-2根号5/5
cosα=-根号5/5
tanβ=1/3
sinβ=根号10/10
cosβ=3根号10/10
sin(α-β)=sinαcosβ-cosαsinβ
=-6根号50/50+根号50/50
=-5根号50/50
=-根号2/2
α-β=5π/4