求f(x)=sin(x/2)+cos(x/2)的单调增区间
问题描述：
求f(x)=sin(x/2)+cos(x/2)的单调增区间
答
f(x)=sin(x/2)+cos(x/2)
=√2sin(x/2+π/4)
单增:
x/2+π/4∈[2kπ-π/2,2kπ+π/2]
x∈[4kπ-3π/2,4kπ+π/2] k∈z