Werner Formula for Sine by Sine/Examples/2 Sine 10 Sine 30
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Example of Use of Werner Formula for Sine by Sine
- $2 \sin 10 \degrees \sin 30 \degrees = \cos 20 \degrees - \cos 40 \degrees$
Proof
\(\ds 2 \sin 10 \degrees \sin 30 \degrees\) | \(=\) | \(\ds \map \cos { {10 \degrees} - {30 \degrees} } - \map \cos { {10 \degrees} + {30 \degrees} }\) | Werner Formula for Sine by Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \map \cos {-20 \degrees} - \cos 40 \degrees\) | evaluating | |||||||||||
\(\ds \) | \(=\) | \(\ds \cos 20 \degrees - \cos 40 \degrees\) | Cosine Function is Even |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $7$.