²表示平方
y=sin(2x+3π/4)+cos²(2x-π/4)
= sin[π+(2x-π/4)】+ {1-sin²(2x-π/4)}
= - sin(2x-π/4) + 1 - sin²(2x-π/4)
= - sin²(2x-π/4) - sin(2x-π/4) + 1
= - {sin(2x-π/4)+1/2}² + 5/4
-1≤sin(2x-π/4)≤1
-1/2≤sin(2x-π/4)+1/2≤3/2
-9/4≤ {sin(2x-π/4)+1/2}²≤0
-1≤ {sin(2x-π/4)+1/2}²≤5/4
值域【-1,5/4】