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Proposition: Additivity Theorems of Cosine and Sine

For the cosine and sine functions, the following additivity theorems hold for all real numbers $x,y\in\mathbb R$:

$$\begin{array}{rcl}\cos(x+y)&=&\cos(x)\cos(y)-\sin(x)\sin(y),\\\sin(x+y)&=&\sin(x)\cos(y)+\cos(x)\sin(y).\end{array}$$

Table of Contents

Proofs: 1

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Examples: 1
Proofs: 2 3

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983