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

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 $\text {XXXII}$: $7$.