若根号3sinx-cosx=sinx+根号3cosx且X属于（0,π）,则X=

若根号3sinx-cosx=sinx+根号3cosx且X属于（0,π）,则X=
若根号3sinx-cosx=sinx+根号3cosx且X属于（0,π）,则X=

若根号3sinx-cosx=sinx+根号3cosx且X属于（0,π）,则X=
√3sinx-cosx=sinx+√3cosx两边同时处以2得
√3sinx/2-cosx/2=sinx/2+√3cosx/2
sinxcos(π/6)-cosxsin(π/6)=sinxcos(π/3)+cosxsin(π/3)
sin(x-π/6)=sin(x+π/3)
因为x∈（0,π）且x-π/6≠x+π/3 所以x-π/6+x+π/3=π
所以x=5π/12