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Fungrim entry: 3ea11b

atan(x)+atan(y)=atan ⁣(x+y1xy)\operatorname{atan}(x) + \operatorname{atan}(y) = \operatorname{atan}\!\left(\frac{x + y}{1 - x y}\right)
Assumptions:xCandyCandx<1andy<1x \in \mathbb{C} \,\mathbin{\operatorname{and}}\, y \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|x\right| < 1 \,\mathbin{\operatorname{and}}\, \left|y\right| < 1
Alternative assumptions:xRandyRandxy<1x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \,\mathbin{\operatorname{and}}\, x y < 1
TeX:
\operatorname{atan}(x) + \operatorname{atan}(y) = \operatorname{atan}\!\left(\frac{x + y}{1 - x y}\right)

x \in \mathbb{C} \,\mathbin{\operatorname{and}}\, y \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|x\right| < 1 \,\mathbin{\operatorname{and}}\, \left|y\right| < 1

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \,\mathbin{\operatorname{and}}\, x y < 1
Definitions:
Fungrim symbol Notation Short description
Atanatan(z)\operatorname{atan}(z) Inverse tangent
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("3ea11b"),
    Formula(Equal(Add(Atan(x), Atan(y)), Atan(Div(Add(x, y), Sub(1, Mul(x, y)))))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC), Less(Abs(x), 1), Less(Abs(y), 1)), And(Element(x, RR), Element(y, RR), Less(Mul(x, y), 1))))

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2019-11-19 15:10:20.037976 UTC