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Fungrim entry: e69cf6

sin ⁣(a)sin ⁣(b)=2cos ⁣(a+b2)sin ⁣(ab2)\sin\!\left(a\right) - \sin\!\left(b\right) = 2 \cos\!\left(\frac{a + b}{2}\right) \sin\!\left(\frac{a - b}{2}\right)
Assumptions:aCandbCa \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
TeX:
\sin\!\left(a\right) - \sin\!\left(b\right) = 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
Sinsin ⁣(z)\sin\!\left(z\right) Sine
CCC\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))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC