lim(x→0)(tanx - sinx)/(sinx*sinx*sinx)
=lim(x→0)(1/cos x-1)/(sin x*sin x)
=lim(x→0)(1-cos x)/(cos x*sin x*sin x)
=lim(x→0)(2-2cos x)/(sin 2x*sin x)
=lim(x→0)(2-2cos x)'/(sin 2x*sin x)'
=lim(x→0)(2sin x)/(2cos 2x*sin x+sin 2x*cos x)
=lim(x→0)2/(2cos 2x+2cos x*cos x)
=2/(2cos 0+2cos0*cos0)
=1/2.