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

Sine