a=sinx,b=cosx
f(x)=a^4+2ab+b^4=(a^2+b^2)^2-2a^2b^2+2ab=1-2(a^2b^2-ab)=3/2-2(ab-1/2)^2
ab=1/2时,即sin2x=1时,取最大值3/2