y=sin α-cos(π/6-α)
=sinα-cosπ/6cosα-sinπ/6sinα
=sinα-√3/2cosα-1/2inα
=-√3/2cosα+1/2inα
=-cosπ/6cosα+sinπ/6sinα
=-cos(π/6+α)
Ymax=1,此时,π/6+α=kπ,即α=kπ-π/6