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Question

Solve : limxπ4(tanx1)(xπ4)

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Solution

limxπ4(tanx1)(xπ4)= limxπ4(tanx1)(1+tanx)(xπ4)(1+tanx)

=limxπ40(tanxtanπ4)(1+tanx)(xπ4)(1+tanπ4.tanx)

=limxπ40(tan(xπ4))(1+tanx)(xπ4)

=limxπ40(tan(xπ4))(xπ4).limxπ40(1+tanx)

=1×(1+tanπ4)

=1+1=2

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