# Proving half-angle formulae Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Looking again

Take another look at the identities.

$\cos^2 \frac{\theta}{2} \equiv \frac{1}{2}(1+\cos \theta) \quad \quad \quad \sin^2 \frac{\theta}{2} \equiv \frac{1}{2}(1-\cos \theta)$

The first says that $\cos^2 \frac{\theta}{2}$ is the mean of $1$ and $\cos \theta$. What does this tell you geometrically?

Can you use the same ideas to think about the identity for $\sin^2 \frac{\theta}{2}$?

Can you draw a diagram to illustrate the following results for $\tan \frac{\theta}{2}$? $\tan \frac{\theta}{2} \equiv \frac{\sin \theta}{1+\cos \theta}$ and $\tan \frac{\theta}{2}\equiv \frac{1-\cos \theta}{\sin \theta}$

For which values of $\theta$ are these identities true?