解法一：原式=lim(x->1)[(1-x)sin(πx/2)/cos(πx/2)]={lim(x->1)[sin(πx/2)]}*{lim(x->1)[(1-x)/cos(πx/2)]}=1*{lim(x->1)[(1-x)/cos(πx/2)]}=lim(x->1)[(1-x)/sin(π/2-πx/2)] (应用诱导公式)=lim(x->1)[(1-x)...