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Fungrim entry: 012eba

sin⁡ ⁣(a)cos⁡ ⁣(b)=sin⁡ ⁣(a+b)+sin⁡ ⁣(a−b)2\sin\!\left(a\right) \cos\!\left(b\right) = \frac{\sin\!\left(a + b\right) + \sin\!\left(a - b\right)}{2}
Assumptions:a∈C and⁡ b∈Ca \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
TeX:
\sin\!\left(a\right) \cos\!\left(b\right) = \frac{\sin\!\left(a + b\right) + \sin\!\left(a - b\right)}{2}

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("012eba"),
    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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2019-06-18 07:49:59.356594 UTC