∵y= cosx + sinx (x∈R)利用辅助角公式得：y= √2 sin(x+π/4) (x∈R)∴最小正周期T= 2π/1 =2π∵y在(x+π/4)∈[2kπ-π/2 ,2kπ+π/2] (k∈Z)上单调递增即x∈[2kπ-3π/4 ,2kπ+π/4] (k∈Z)时y单调递增∴该函数周期为2π，递增区间为x∈[2kπ-3π/4 ,2kπ+π/4] (k∈Z)
辅助角公式学过没有？
