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Question

limxi1+cosxtan2x

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Solution

limxi1+cosxtan2x

xπ,xπ0, let y=xπ

y0

=limy01+cosx(π+y)tan2(π+y)

=limy01cosytan2y

=limy02sin2y2tan2y

=2(limy0siny2y2)×y24×1(limy0tan yy)2×y2

=2×1×14×11

[limθ0sinθθ=1 and limθ0tanθθ=1]

=12


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