(1)f(x)=sin(x+π/6)+sin(x-π/6)-cos2x+m (积化和差)=2sinx·cosπ/6-cos2x+m (和差角公式、消项)=2sin²x+√3sinx+m-1=> t=2π (2)x∈[-π/4,π/4]=> sinx∈[-√2/2,√2/2]以sinx为自变量的抛物线的对称轴横坐标为-√3/4∈[-√2/2,√2/2],于是2×(-√3/4)²+√3(-√3/4)+m-1=-3解得m=-13/8