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Fungrim entry: 6c3ba9

sin ⁣(z)cos ⁣(z)=2sin ⁣(zπ4)\sin\!\left(z\right) - \cos\!\left(z\right) = \sqrt{2} \sin\!\left(z - \frac{\pi}{4}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\sin\!\left(z\right) - \cos\!\left(z\right) = \sqrt{2} \sin\!\left(z - \frac{\pi}{4}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
Sqrtz\sqrt{z} Principal square root
ConstPiπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("6c3ba9"),
    Formula(Equal(Sub(Sin(z), Cos(z)), Mul(Sqrt(2), Sin(Sub(z, Div(ConstPi, 4)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-25 15:30:03.056001 UTC