f(x)=-f(x-4)=f(x-8),周期为8.
tanα=2,sinαcosα=sinαcosα/[(sinα)^2+(cosα)^2]=tanα/[(tanα)^2+1]=2/5
f(2010sinαcosα)=f(804)=f(100*8+4)=f(4)=-f(0)=-3