limx→π41−tan xx−π4
limx→π41−tan xx−π4
Let x=π4+y
⇒y=x−π4asx→π4=y→0
=limy→01−tan(y+π4)y
=limy→01−(tan y+tanπ41−tan y tanπ4)y
=limy→01−tan y+11−tan yy
=limy→0(1−tan y−tan y−1)y(1−tan y)
[∵tan π4=1]
=limy→0(−2 tan y)y(1−tan y)
=−2limy→0tan yy×1limy→0(1−tan y)
=−2×11(1−0)=−2