令a=1-x
a趋于0
tan(1-a)π/2
=tan(π/2-aπ/2)
=cot(aπ/2)
=1/tan(aπ/2)
x趋于0时,tanx~x
所以tan （aπ/2)~aπ/2
所以原式=lima/tan(aπ/2)
=lima/(aπ/2)
=2/π