Fungrim entry: acf63c

$\sin^{2}\!\left(z\right) = \frac{\tan^{2}\!\left(z\right)}{1 + \tan^{2}\!\left(z\right)}$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \notin \left\{ \frac{\left(2 n + 1\right) \pi}{2} : n \in \mathbb{Z} \right\}$
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
Pow${a}^{b}$ Power
Sin$\sin\!\left(z\right)$ Sine
CC$\mathbb{C}$ Complex numbers
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
ConstPi$\pi$ The constant pi (3.14...)
ZZ$\mathbb{Z}$ 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))))))

Topics using this entry

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