Fungrim entry: 00e608

\operatorname{atan}(x) - \operatorname{atan}(y) = \operatorname{atan2}\!\left(x - y, 1 + x y\right)

Assumptions:

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}

TeX:

\operatorname{atan}(x) - \operatorname{atan}(y) = \operatorname{atan2}\!\left(x - y, 1 + x y\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`Atan2`	$\operatorname{atan2}\!\left(y, x\right)$	Two-argument inverse tangent
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("00e608"),
    Formula(Equal(Sub(Atan(x), Atan(y)), Atan2(Sub(x, y), Add(1, Mul(x, y))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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