Werner Formula for Sine by Cosine/Examples/2 Sine 30 Cosine 10

Example of Use of Werner Formula for Sine by Cosine

$2 \sin 30 \degrees \cos 10 \degrees = \sin 40 \degrees + \sin 20 \degrees$

Proof

\(\ds 2 \sin 30 \degrees \cos 10 \degrees\)

\(=\)

\(\ds \map \sin { {30 \degrees} + {10 \degrees} } + \map \sin { {30 \degrees} - {10 \degrees} }\)

Werner Formula for Sine by Cosine

\(\ds \)

\(=\)

\(\ds \sin 40 \degrees + \sin 20 \degrees\)

evaluating

$\blacksquare$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $10$.