用等价无穷小做:当x→0时 1-cos(2x)~(1/2)x²sin(x)~x所以 lim(x→0)(1-cos2x)/xsinx=lim(x→0) (x^2/2)/x^2=1/2
lim(x→0)(1-cos2x)/xsinx=lim(x→0) (x^2/2)/x^2=1/2
=lim{1-[1-2(sinx)^2]}/xsinx=lim2sinx/x=2