Fungrim entry: ad6c1c

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

Assumptions:

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

TeX:

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

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

Definitions:

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

Source code for this entry:

Entry(ID("ad6c1c"),
    Formula(Equal(Mul(Sin(a), Sin(b)), Div(Sub(Cos(Sub(a, b)), Cos(Add(a, b))), 2))),
    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