求极限limx→1(1-x)tan(πx/2)．

求极限limx→1(1-x)tan(πx/2)．
【正确答案】：原式=limx→1={(1-x)sin(π/2)x/[cos(π/2)x]}=limx→1sin(π/2)x limx→1{π/2(1-x)/{sin[π/2(1-x)]}}(2/π)=2/π.