求cosπxcos(πx-π/3)+sin^2πx的周期单调区间和值域

问题描述:

求cosπxcos(πx-π/3)+sin^2πx的周期单调区间和值域

令πx=α.则cosπxcos(πx-π/3)+sin^2πx =cosα·cos(α-π/3)+sin²α =cosα·[cosα·cosπ/3+sinα·sinπ/3]+(1-cos2α)/2 =(cos²α)/2+√3sinα...