2cos(2x+π/4)≥1,即:cos(2x+π/4)≥1/2
则:2kπ-π/3≤2x+π/4≤2kπ+π/3
kπ-7π/24≤x≤kπ+π/24
则这个不等式的解集是:{x|kπ-7π/24≤x≤kπ+π/24,k∈Z}