設函數f(x)=sin(wx+2π/3)+sin(wx-2π/3)(w>0)的最小正週期為π,求函數的單調區間?

設函數f(x)=sin(wx+2π/3)+sin(wx-2π/3)(w>0)的最小正週期為π,求函數的單調區間?

f(x)=sin(wx+2π/3)+sin(wx-2π/3)=sinwxcos(2π/3)+coswxsin(2π/3)+sinwxcos(2π/3)-coswxsin(2π/3)=sinwxcos(2π/3)+sinwxcos(2π/3)=2sinwxcos(2π/3)=-sinwx∵T=π∴2π/w=πw=2∴函數為f(x)=-sin2x∴函數的單…