x→0 lim (1-cos ax)/(sinx)^2
=x→0 lim (a*sin ax)/(2sinx*cosx)
=x→0 lim (a*sin ax)/sin2x
=x→0 lim (a^2*cos ax)/2cos2x
=(a^2*1)/(2*1)
=(a^2)/2
就是用两次洛必达法则就行了