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Fungrim entry: f6d0c6

sin2 ⁣(a)cos2 ⁣(b)=cos ⁣(a+b)cos ⁣(ab)\sin^{2}\!\left(a\right) - \cos^{2}\!\left(b\right) = -\cos\!\left(a + b\right) \cos\!\left(a - b\right)
Assumptions:aC  and  bCa \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
\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}
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Sinsin(z)\sin(z) Sine
Coscos(z)\cos(z) Cosine
CCC\mathbb{C} Complex numbers
Source code for this entry:
    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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2021-03-15 19:12:00.328586 UTC