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Fungrim entry: 47331d

atan ⁣(x+y)atan(x)=atan2 ⁣(y,1+x(x+y))\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}(x)\right| = \operatorname{atan2}\!\left(\left|y\right|, 1 + x \left(x + y\right)\right)
Assumptions:xR  and  yRx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
TeX:
\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}(x)\right| = \operatorname{atan2}\!\left(\left|y\right|, 1 + x \left(x + y\right)\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Atanatan(z)\operatorname{atan}(z) 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("47331d"),
    Formula(Equal(Abs(Sub(Atan(Add(x, y)), Atan(x))), Atan2(Abs(y), Add(1, Mul(x, Add(x, y)))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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2020-08-27 09:56:25.682319 UTC