May 16th, 2017, 12:31 PM  #1 
Member Joined: Dec 2016 From:  Posts: 54 Thanks: 10  Formula of arctan(tan(x))
Does the formula $\arctan(\tan(x))=x$ hold only for $x\in(\pi/2,+\pi/2)$, and how can this be extended to other values of x? Thanks!

May 17th, 2017, 04:07 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,944 Thanks: 797 
Since tan(x) is not a "one to one" function, strictly speaking it does not have an inverse function so we restrict it to one "period", between and . Then arctan is defined as giving a value between those.


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arctantanx, formula 
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