limx→π4tan2xcot(x-π4)=______．

题型：不详难度：来源：

lim

x→ π 4

tan2x

cot(x- π 4 )

=______．

答案

lim

x→ π 4

tan2x

cot(x- π 4 )

=

lim

x→ π 4

2 2 sin2x(sinx-cosx)

2 2 cos2x( cosx+ sinx)

=

lim

x→ π 4

(- 

sin2x

1+sin2x

)=-

sin π 2

1+sin π 2

=-

1

2

故答案为：-

1

2