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May 16th, 2017, 11:31 AM   #1
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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!
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May 17th, 2017, 03:07 AM   #2
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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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