f（x)＝(sinx＋cosx）²＋cos2x
=sin²x＋cos²x+2sinxcosx＋cos2x
=1+sin2x＋cos2x
=1+√2sin(2x+π/4)
f（π/4）=1+1+0=2
f（x）的递增区间
2Kπ-π/2≤2x+π/4≤2K+π/2 ,K∈Z
Kπ-3π/8≤x≤Kπ+π/8 ,K∈Z