Cosine minus Cosine/Examples/Cosine 20 minus Cosine 50
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Example of Use of Cosine minus Cosine
- $\cos 20 \degrees - \cos 50 \degrees = 2 \sin 50 \degrees \cos 10 \degrees$
Proof
| \(\ds \cos 20 \degrees - \cos 50 \degrees\) | \(=\) | \(\ds -2 \map \sin {\dfrac { {20 \degrees} + {50 \degrees} } 2} \map \sin {\dfrac { {20 \degrees} - {50 \degrees} } 2}\) | Cosine minus Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds -2 \sin 35 \degrees \map \sin {-15 \degrees}\) | evaluating | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \sin 35 \degrees \sin 15 \degrees\) | Sine Function is Odd |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $2$.