Fungrim home page

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:zC  and  z{(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\}
\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\}
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
Piπ\pi The constant pi (3.14...)
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(Pow(Sin(z), 2), Div(Pow(Tan(z), 2), Add(1, Pow(Tan(z), 2))))),
    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