因为cos(2x)=1-2 sin^2(x),
所以sin^2(x)=[1-cos(2x)]/2.
y=1/2sin(2x)+sin^2(x)
=1/2sin(2x)+ [1-cos(2x)]/2
=1/2*sin(2x)- 1/2*cos(2x)+1/2
=√2/2*[√2/2* sin(2x)- √2/2* cos(2x)] +1/2
=√2/2* sin(2x-π/4) +1/2
∴函数值域是[-√2/2+1/2,√2/2+1/2].