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Fungrim entry: f6d0c6

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

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Sinsin⁡ ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f6d0c6"),
    Formula(Equal(Sub(Pow(Sin(a), 2), Pow(Cos(b), 2)), Mul(Neg(Cos(Add(a, b))), Cos(Sub(a, b))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC))))

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2019-06-18 07:49:59.356594 UTC