函数Y=SIN2X+COS2X的值域?
解：y=sin2x+cos2x=√2(sin2x*√2/2+cos2x*√2/2)
=√2[sin2xcos(π/4)+cos2xsin(π/4)]
=√2sin（2x+π/4)
因为 sinx∈[-1,1] (为什么 sinx∈[-1,1）谢谢
sin（2x+π/4)∈[-1,1]
所以 √2sin（2x+π/4)∈[-√2,√2]
y∈[-√2,√2]
即函数值域是[-√2,√2]π/4