Fungrim entry: f6d0c6

\sin^{2}\!\left(a\right) - \cos^{2}\!\left(b\right) = -\cos\!\left(a + b\right) \cos\!\left(a - b\right)

Assumptions:

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}

TeX:

\sin^{2}\!\left(a\right) - \cos^{2}\!\left(b\right) = -\cos\!\left(a + b\right) \cos\!\left(a - b\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`Sin`	$\sin(z)$	Sine
`Cos`	$\cos(z)$	Cosine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f6d0c6"),
    Formula(Equal(Sub(Pow(Sin(a), 2), Pow(Cos(b), 2)), Mul(Neg(Cos(Add(a, b))), Cos(Sub(a, b))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC))))

Topics using this entry

Sine

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