设α,β,γ∈(0,π/2),且sinα+sinγ-sinβ=0,cosβ+cosγ-cosα=0,求α-β的值

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设α,β,γ∈(0,π/2),且sinα+sinγ-sinβ=0,cosβ+cosγ-cosα=0,求α-β的值设α,β,γ∈(0,π/2),且sinα+sinγ-sinβ=0,cosβ+cosγ-c

设α,β,γ∈(0,π/2),且sinα+sinγ-sinβ=0,cosβ+cosγ-cosα=0,求α-β的值
设α,β,γ∈(0,π/2),且sinα+sinγ-sinβ=0,cosβ+cosγ-cosα=0,求α-β的值

设α,β,γ∈(0,π/2),且sinα+sinγ-sinβ=0,cosβ+cosγ-cosα=0,求α-β的值
sinγ=sinβ-sinα
cosγ=cosα-cosβ
sinγ^2+cosγ^2
=(sinβ-sinα)^2+(cosα-cosβ)^2
=2-2sinαsinβ-2cosαcosβ
=2-2(sinαsinβ+cosαcosβ)
=2-2cos(α-β)
=1
=>cos(α-β)=1/2
α-β=π/3

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