Cosine of 72 Degrees/Proof 1
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Theorem
- $\cos 72 \degrees = \cos \dfrac {2 \pi} 5 = \dfrac {\sqrt 5 - 1} 4$
Proof
\(\ds \cos 72 \degrees\) | \(=\) | \(\ds \map \cos {90 \degrees - 18 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \sin 18 \degrees\) | Cosine of Complement equals Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {\sqrt 5 - 1} 4\) | Sine of $18 \degrees$ |
$\blacksquare$