Werner Formula for Cosine by Sine/Examples/2 Cosine 2 A Sine 4 A
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Example of Use of Werner Formula for Cosine by Sine
- $2 \cos 2 A \sin 4 A = \sin 6 A + \sin 2 A$
Proof
| \(\ds 2 \cos 2 A \sin 4 A\) | \(=\) | \(\ds \map \sin {2 A + 4 A} - \map \sin {2 A - 4 A}\) | Werner Formula for Cosine by Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin 6 A - \map \sin {-2 A}\) | evaluating | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin 6 A + \sin 2 A\) | Sine Function is Odd |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $12$.