Fungrim entry: e69cf6

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

Assumptions:

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

TeX:

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

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("e69cf6"),
    Formula(Equal(Sub(Sin(a), Sin(b)), Mul(Mul(2, Cos(Div(Add(a, b), 2))), Sin(Div(Sub(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