f(x）=sin^4x+cos^2x+1/4sin2xcos2x
=(1/4)[1-cos2x]^2+1/2(cos2x+1)+(1/8)sin4x
=(1/4)-(1/2)cos2x+(1/4)(cos2x)^2+(1/2)cos2x+1/2+(1/8)sin4x
=3/4+(1/8)(1+cos4x)+(1/8)sin4x
=7/8+(1/8)(cos4x+sin4x)
=(√2/8)sin(4x+π/4)+7/8
其最小正周期T=2π/4=π/2