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Fungrim entry: 012eba

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

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(Mul(Sin(a), Cos(b)), Div(Add(Sin(Add(a, b)), Sin(Sub(a, b))), 2))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC))))

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2021-03-15 19:12:00.328586 UTC