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Fungrim entry: 0b829e

cos ⁣(atan(z))=11+z2\cos\!\left(\operatorname{atan}(z)\right) = \frac{1}{\sqrt{1 + {z}^{2}}}
Assumptions:zC{i,i}z \in \mathbb{C} \setminus \left\{-i, i\right\}
TeX:
\cos\!\left(\operatorname{atan}(z)\right) = \frac{1}{\sqrt{1 + {z}^{2}}}

z \in \mathbb{C} \setminus \left\{-i, i\right\}
Definitions:
Fungrim symbol Notation Short description
Atanatan(z)\operatorname{atan}(z) Inverse tangent
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("0b829e"),
    Formula(Equal(Cos(Atan(z)), Div(1, Sqrt(Add(1, Pow(z, 2)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(Neg(ConstI), ConstI)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-01-31 18:09:28.494564 UTC