limx→i1+cosxtan2x
⇒x→π,x−π→0, let y=x−π
⇒y→0
=limy→01+cosx(π+y)tan2(π+y)
=limy→01−cosytan2y
=limy→02sin2y2tan2y
=2(limy→0siny2y2)×y24×1(limy→0tan yy)2×y2
=2×1×14×11
[∵limθ→0sinθθ=1 and limθ→0tanθθ=1]
=12