=lim（x→0）x^2/2*[x-ln（1+tanx）]/[x^4]
=lim（x→0）[x-ln（1+tanx）]/[2x^2]
=lim（x→0）[1-secx^2/(1+tanx)]/(4x)
=lim（x→0）(1+tanx-secx^2)/[4(1+tanx)sinx]
=lim（x→0）(cosx^2+cosx*sinx-1)/[4(1+tanx)sinxcosx^2]
=lim（x→0）(cosx-sinx)/[4(1+tanx)cosx^2]
=1/4