Double Angle Formulas/Cosine/Proof 2
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Theorem
- $\cos 2 \theta = \cos^2 \theta - \sin^2 \theta$
Proof
| \(\ds \cos 2 \theta\) | \(=\) | \(\ds \map \cos {\theta + \theta}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \cos \theta \cos \theta - \sin \theta \sin \theta\) | Cosine of Sum | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cos^2 \theta - \sin^2 \theta\) |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: The addition formulae