Fungrim entry: 0b829e

\cos\!\left(\operatorname{atan}(z)\right) = \frac{1}{\sqrt{1 + {z}^{2}}}

Assumptions:

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
`Cos`	$\cos(z)$	Cosine
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`ConstI`	$i$	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)))))

Topics using this entry

Inverse tangent

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

2021-03-15 19:12:00.328586 UTC