ln(sinx)^tan^2(x)=tan^2(x)ln(sinx)=(1/cos^2(x)-1)ln(sinx)
此式极限=lim[ln(sinx)/cos^2(x)-ln(sinx)]=lim[ln(sinx)/cos^2(x)]
=lim[1/sinx*cosx/(2cosx*(-sinx))]=lim[-1/2sin^2(x)]=-1/2
∴原式=e^(-1/2)