Sine plus Sine/Examples/Sine 2 A plus Sine 6 A
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Example of Use of Sine plus Sine
- $\sin 2 A + \sin 6 A = 2 \sin 4 A \cos 2 A$
Proof
| \(\ds \sin 2 A + \sin 6 A\) | \(=\) | \(\ds 2 \map \sin {\dfrac {2 A + 6 A} 2} \map \cos {\dfrac {2 A - 6 A} 2}\) | Sine plus Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \sin 4 A \map \cos {-2 A}\) | evaluating | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \sin 4 A \cos 2 A\) | Cosine Function is Even |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $5$.