Double Angle Formula for Cosine/Corollary 5

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 $(25)$