高数一道求极限的题目~

(1-x)tg(pix/2)
=(1-x)sin(pix/2)/cos(pix/2)
变量替换y=1-x
化为y趋于0时的极限
ysin(pi(1-y)/2)/cos(pi(1-y)/2)
=ycos(piy/2)/sin(piy/2)
=cos(piy/2)*(piy/2)/sin(piy/2)*(2/pi)
由于sinx/x趋于1,当x趋于0时
则上式趋于cos0*1*(2/pi)=2/pi