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Fungrim entry: d59bd9

sin(a)+sin(b)=2sin ⁣(a+b2)cos ⁣(ab2)\sin(a) + \sin(b) = 2 \sin\!\left(\frac{a + b}{2}\right) \cos\!\left(\frac{a - b}{2}\right)
Assumptions:aC  and  bCa \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
\sin(a) + \sin(b) = 2 \sin\!\left(\frac{a + b}{2}\right) \cos\!\left(\frac{a - b}{2}\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Coscos(z)\cos(z) Cosine
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Add(Sin(a), Sin(b)), Mul(Mul(2, Sin(Div(Add(a, b), 2))), Cos(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.

2021-03-15 19:12:00.328586 UTC