Werner Formula for Cosine by Cosine/Examples/2 Cosine 20 Cosine 50

Example of Use of Werner Formula for Cosine by Cosine

$2 \cos 20 \degrees \cos 50 \degrees = \cos 30 \degrees + \cos 70 \degrees$

Proof

\(\ds 2 \cos 20 \degrees \cos 50 \degrees\)

\(=\)

\(\ds \map \cos { {20 \degrees} - {50 \degrees} } + \map \cos { {20 \degrees} + {50 \degrees} }\)

Werner Formula for Cosine by Cosine

\(\ds \)

\(=\)

\(\ds \map \cos {-30 \degrees} + \cos 70 \degrees\)

evaluating

\(\ds \)

\(=\)

\(\ds \cos 30 \degrees + \cos 70 \degrees\)

Cosine Function is Even

$\blacksquare$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $8$.