热心网友

y=(1/2)cos(πx+π/3)-sin(πx+5π/6)=(1/2)[(1/2)cosπx-(√3/2)sinπx]-[(-√3/2)sinπx+(1/2)cosπx]=(1/2)[(√3/2)sinπx-(1/2)cosπx]=(1/2)sin[πx-(π/3)]所以递增区间为：2kπ-π/2≤πx-(π/3)≤2kπ+π/22k-1/2≤x-(1/3)≤2k+1/22k-1/6≤x≤2k+5/6既递增区间为: [2k-(1/6),2k+(5/6)],k∈Z