令a=π-x
则a→0
所以原式=lim(a→0)atan[(π-a)/2]
=lim(a→0)acot(a/2)
=lim(a→0)acos(a/2)/sin(a/2)
=lim(a→0)2*[(a/2)/sin(a/2)]*cos(a/2)
=2*1*cos0
=2