3sinx-根号3cosx=2根号3sin（x+α）.α属于（-π,π）,则α的值是

3sinx-根号3cosx=2根号3sin（x+α）.α属于（-π,π）,则α的值是
3sinx-根号3cosx=2根号3sin（x+α）.α属于（-π,π）,则α的值是

3sinx-根号3cosx=2根号3sin（x+α）.α属于（-π,π）,则α的值是
左边=2√3(sinx*√3/2-cosx*1/2)
=2√3(sinxcosπ/6+cosxsinπ/6)
=2√3sin(x-π/6)
所以α=-π/6

3sinx-根号3cosx
=根号3^2+3sin(x+arctan(-根号3/3))
=2根号2sin(x+arctan(-根号3/3))
α=arctan(-根号3/3)
α属于（-π，π）
α=-π/6,α=5π/6

3sinx-根号3cosx=2根号3sin（x+α)
√3/2sinx-1/2cosx=sin(x+a)
sin(x-30)=sin(x+a)
x-30=x+a,a=-π/6