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Hi Amelia,

This is a tricky question and Jonny G is correct in saying there is an error in your statement - it should be pi/2. The outline for proving this is to assume x=tan(y)

This implies that arctan(x)=y.      [I prefer arctan to tan^-1 ]

Now there is a general formula tan(y)=cot(pi/2-y).

Thus arctan(x)+arccot(x)

=arctan(tan(y))+arccot(tany)

=arctan(tan(y))+arccot(cot(pi/2-y))=y+pi/2-y=pi/2 QED

If you look at the diagram below; where can we see tan^-1(x)? Where can we see cot^-1 (x)? Can we prove (almost) what you state now? (I think there is an error in what you are trying to prove!) Jonny

ps I'm assuming that by tan^-1(x) you mean arctan(x).