取对数
ln原式=lim(x→0)sinxln(tanx)
=lim(x→0)ln(tanx)/(1/sinx)
=lim(x→0)(1/tanx*1/cos^2(x))/(-1/sin^2(x)*cosx)
=lim(x→0)(1/(sinxcosx))/(-cosx/sin^2(x))
=lim(x→0)-sinx/cos^2(x)
=0
所以原式=e^0=1