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Fungrim entry: 00e608

atan⁡ ⁣(x)−atan⁡ ⁣(y)=atan2⁡ ⁣(x−y,1+xy)\operatorname{atan}\!\left(x\right) - \operatorname{atan}\!\left(y\right) = \operatorname{atan2}\!\left(x - y, 1 + x y\right)
Assumptions:x∈R and⁡ y∈Rx \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R}
TeX:
\operatorname{atan}\!\left(x\right) - \operatorname{atan}\!\left(y\right) = \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
Atanatan⁡ ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
Atan2atan2⁡ ⁣(y,x)\operatorname{atan2}\!\left(y, x\right) Two-argument inverse tangent
RRR\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))))

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2019-06-18 07:49:59.356594 UTC