y=1/2*sin2x+(1+cos2x)/2
=1/2*(sin2x+cos2x)+1/2
=√2/2*sin(2x+π/4)+1/2
所以T=2π/2=π
sin(2x+π/4）递增则
2kπ-π/2<2x+π/4<2kπ+π/2
kπ-3π/8所以增区间是(kπ-3π/8,kπ+π/8)