y=[2(cosx)^2+1+2cosxsinx-1]/2
=[2(cosx)^2-1+2cosxsinx+1]/2
=[cos(2x)+sin(2x)+1]/2
=[√2sin(2x+π/4)+1]/2
∵-1≤sin(2x+π/4)≤1
∴(1-√2)/2≤y≤(1+√2)/2