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Fungrim entry: 508e2c

sin ⁣(ab)=sin ⁣(a)cos ⁣(b)cos ⁣(a)sin ⁣(b)\sin\!\left(a - b\right) = \sin\!\left(a\right) \cos\!\left(b\right) - \cos\!\left(a\right) \sin\!\left(b\right)
Assumptions:aCandbCa \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
\sin\!\left(a - b\right) = \sin\!\left(a\right) \cos\!\left(b\right) - \cos\!\left(a\right) \sin\!\left(b\right)

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Sin(Sub(a, b)), Sub(Mul(Sin(a), Cos(b)), Mul(Cos(a), Sin(b))))),
    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.

2019-08-25 15:30:03.056001 UTC