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lim x--->pi/4 tanx - cotx / x - pi/4

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I assume you have this:

LIM (tanx-cotx)/(x-PI/4) as x>>PI/4

which has a limit in the form of 0/0

L'Hopital's rule

= lim (sec^2x+csc^2x)/(-PI/4) which you can easily evaluate as x>>PI/4

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