Double Angle Formulas/Cosine/Corollary 1
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Corollary to Double Angle Formula for Cosine
- $\cos 2 \theta = 2 \ \cos^2 \theta - 1$
where $\cos$ denotes cosine.
Proof
| \(\displaystyle \cos 2 \theta\) | \(=\) | \(\displaystyle \cos^2 \theta - \sin^2 \theta\) | Double Angle Formula for Cosine | ||||||||||
| \(\displaystyle \) | \(=\) | \(\displaystyle \cos^2 \theta - \paren {1 - \cos^2 \theta}\) | Sum of Squares of Sine and Cosine | ||||||||||
| \(\displaystyle \) | \(=\) | \(\displaystyle 2 \ \cos^2 \theta - 1\) |
$\blacksquare$
Also see
- Square of Cosine: $\cos^2 \theta = \dfrac {1 + \cos 2 \theta} 2$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: $5.39$
