Double Angle Formulas/Cosine/Corollary 1/Proof
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Corollary to Double Angle Formula for Cosine
- $\cos 2 \theta = 2 \cos^2 \theta - 1$
Proof
| \(\ds \cos 2 \theta\) | \(=\) | \(\ds \cos^2 \theta - \sin^2 \theta\) | Double Angle Formula for Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cos^2 \theta - \paren {1 - \cos^2 \theta}\) | Sum of Squares of Sine and Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \cos^2 \theta - 1\) |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: The addition formulae