Cosine plus Cosine/Examples/Cosine 30 plus Cosine 70
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Example of Use of Cosine plus Cosine
- $\cos 30 \degrees + \cos 70 \degrees = 2 \cos 50 \degrees \cos 20 \degrees$
Proof
| \(\ds \cos 30 \degrees + \cos 70 \degrees\) | \(=\) | \(\ds 2 \map \cos {\dfrac { {30 \degrees} + {70 \degrees} } 2} \map \cos {\dfrac { {30 \degrees} - {70 \degrees} } 2}\) | Cosine plus Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \cos 50 \degrees \map \cos {-20 \degrees}\) | evaluating | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \cos 50 \degrees \cos 20 \degrees\) | Cosine Function is Even |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $3$.