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 $18 \degrees$

$\blacksquare$