Evaluate: limx→π2tan2xx−π2
We have, limx→π2tan2xx−π2
At x=π2, the value of the given function takes the form 00
If, we put x=h+π2 such that x→π2 then h→ 0
Therefore limx→π2tan2xx−π2=limh→ 0tan2(h+π2)h
limh→ 0tan(π+2h)h{ tan(π+θ)=tanθ}
=limh→ 0tan 2hh×22
=2limh→ 0tan 2hh{limx→ 0tan xx+1}
=2× 1=2