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Fungrim entry: acf63c

sin2 ⁣(z)=tan2 ⁣(z)1+tan2 ⁣(z)\sin^{2}\!\left(z\right) = \frac{\tan^{2}\!\left(z\right)}{1 + \tan^{2}\!\left(z\right)}
Assumptions:zCandz{(2n+1)π2:nZ}z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \notin \left\{ \frac{\left(2 n + 1\right) \pi}{2} : n \in \mathbb{Z} \right\}
TeX:
\sin^{2}\!\left(z\right) = \frac{\tan^{2}\!\left(z\right)}{1 + \tan^{2}\!\left(z\right)}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \notin \left\{ \frac{\left(2 n + 1\right) \pi}{2} : n \in \mathbb{Z} \right\}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Sinsin ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ConstPiπ\pi The constant pi (3.14...)
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("acf63c"),
    Formula(Equal(Pow(Sin(z), 2), Div(Pow(Tan(z), 2), Add(1, Pow(Tan(z), 2))))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(z, SetBuilder(Div(Mul(Add(Mul(2, n), 1), ConstPi), 2), n, Element(n, ZZ))))))

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

2019-08-25 15:30:03.056001 UTC