My Math Forum Formula of arctan(tan(x))

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 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 $-pi/2$ and $\pi/2$. Then arctan is defined as giving a value between those. Thanks from nietzsche

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