Werner Formula for Cosine by Sine/Examples/2 Cosine 30 Sine 20
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Example of Use of Werner Formula for Cosine by Sine
- $2 \cos 30 \degrees \sin 20 \degrees = \sin 50 \degrees - \sin 10 \degrees$
Proof
| \(\ds 2 \cos 30 \degrees \sin 20 \degrees\) | \(=\) | \(\ds \map \sin { {30 \degrees} + {20 \degrees} } - \map \sin { {30 \degrees} - {20 \degrees} }\) | Werner Formula for Cosine by Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin 50 \degrees - \sin 10 \degrees\) | evaluating |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $9$.