选C
A.把（x+π）代入,则f(x+π)=sin(2x+2π)=sin2x
B.同样代入,则f(π-x)=sin(2π-2x)=sin(-2π)=-f(x)
C 代入,f(π/2+x)=f(π+2x)=-f(x)
D代入,f(x+2π)=sin(2x+4π)=sin2x
而f(2π-x)=sin(4π-2x)=-sin2x
所以选C