limx→0 ln(2-x^2)-ln2)/cosx-1
=lim(x→0) ln(2-x^2)-ln2)/(x^2/2)
=lim(x→0) ln[(2-x^2)/2]/(x^2/2)
=lim(x→0) ln(1-x^2/2)/(x^2/2)
=lim(x→0) (-x^2/2)/(x^2/2)
=-1