Cosine minus Cosine/Examples/Cosine 2 A minus Cosine 4 A
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Example of Use of Cosine minus Cosine
- $\cos 2 A - \cos 4 A = 2 \sin 3 A \sin A$
Proof
| \(\ds \cos 2 A - \cos 4 A\) | \(=\) | \(\ds -2 \map \sin {\dfrac {2 A + 4 A} 2} \map \sin {\dfrac {2 A - 4 A} 2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -2 \sin 3 A \map \sin {-A}\) | evaluating | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \sin 3 A \sin A\) | Sine Function is Odd |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $6$.