Werner Formula for Sine by Sine/Examples/2 Sine 3 A Sine 5 A
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Example of Use of Werner Formula for Sine by Sine
- $2 \sin 3 A \sin 5 A = \cos 2 A - \cos 8 A$
Proof
| \(\ds 2 \sin 3 A \sin 5 A\) | \(=\) | \(\ds \map \cos {3 A - 5 A} - \map \cos {3 A + 5 A}\) | Werner Formula for Sine by Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \map \cos {-2 A} - \cos 8 A\) | evaluating | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cos 2 A - \cos 8 A\) | Cosine Function is Even |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $11$.