# 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$\sin(z)$ Sine
CC$\mathbb{C}$ Complex numbers
Pi$\pi$ 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, Set(Div(Mul(Add(Mul(2, n), 1), Pi), 2), ForElement(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.

2021-03-15 19:12:00.328586 UTC