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

为方便记a=α, b=β, c=γ
则sinc=sinb-sina, cosc=cosb-cosa
sin^2c+cos^2c=1
即(sinb-sina)^2+(cosb-cosa)^2=1
即sin²b-2sinasinb+sin²a+cos²b-2cosacosb+cos²a=1
即2-2(sinasinb+cosacosb)=1
即cos(b-a)=1/2,所以b-a=π/6或者-π/6
由于a,b,c为锐角,因而由sinc=sinb-sina>0知b>a,所以b-a=π/6.

π/3