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Fungrim entry: f516e3

atan ⁣(tan ⁣(θ))=θ\operatorname{atan}\!\left(\tan\!\left(\theta\right)\right) = \theta
Assumptions:θCandπ2<Re ⁣(θ)<π2\theta \in \mathbb{C} \,\mathbin{\operatorname{and}}\, -\frac{\pi}{2} < \operatorname{Re}\!\left(\theta\right) < \frac{\pi}{2}
TeX:
\operatorname{atan}\!\left(\tan\!\left(\theta\right)\right) = \theta

\theta \in \mathbb{C} \,\mathbin{\operatorname{and}}\, -\frac{\pi}{2} < \operatorname{Re}\!\left(\theta\right) < \frac{\pi}{2}
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
CCC\mathbb{C} Complex numbers
ConstPiπ\pi The constant pi (3.14...)
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
Source code for this entry:
Entry(ID("f516e3"),
    Formula(Equal(Atan(Tan(theta)), theta)),
    Variables(theta),
    Assumptions(And(Element(theta, CC), Less(Neg(Div(ConstPi, 2)), Re(theta), Div(ConstPi, 2)))))

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2019-09-16 21:17:18.797188 UTC