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Fungrim entry: f183d0

sin(z)+cos(z)=2sin ⁣(z+π4)\sin(z) + \cos(z) = \sqrt{2} \sin\!\left(z + \frac{\pi}{4}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\sin(z) + \cos(z) = \sqrt{2} \sin\!\left(z + \frac{\pi}{4}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f183d0"),
    Formula(Equal(Add(Sin(z), Cos(z)), Mul(Sqrt(2), Sin(Add(z, Div(Pi, 4)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2019-11-19 15:10:20.037976 UTC