Double Angle Formula for Cosine/Corollary 5
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Corollary to Double Angle Formula for Cosine
- $1 - \cos \theta = 2 \sin^2 \dfrac \theta 2$
Proof
From Double Angle Formula for Cosine: Corollary $2$:
- $\cos 2 \theta = 1 - 2 \sin^2 \theta$
The result follows from substituting $\dfrac \theta 2$ for $\theta$ and rearranging.
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Formulae $(25)$