f(x)=√3/2cos(2x+π/4)+(sinx)^2
=√3/2*(cos2x-sin2x)/√2+(1-cos2x)/2
=(√6/4-1/2)cos2x-(√6/4)sin2x+1/2
=kcos(2x+t)+1/2,
其中k=√[(√6/4-1/2)^2+3/8],t=arcsin[√6/(4k)],
∴f(x)的最小正周期=π.
f(x)=√3/2cos(2x+π/4)+(sinx)^2
=√3/2*(cos2x-sin2x)/√2+(1-cos2x)/2
=(√6/4-1/2)cos2x-(√6/4)sin2x+1/2
=kcos(2x+t)+1/2,
其中k=√[(√6/4-1/2)^2+3/8],t=arcsin[√6/(4k)],
∴f(x)的最小正周期=π.