## Proving Identities – Half angles based on the Double Angle formulae

Some identities work with half angles which are based on the double angle identities.

Double angle identities

- sin 2A ≡ 2sin A cos A

cos 2A ≡ cos^{2}A – sin^{2}A

or

cos 2A ≡ 2cos^{2}A – 1

or

cos 2A ≡ 1 – 2sin^{2}A

tan 2A ≡ (2 tan A) / (1 – tan^{2}A)

## Example 1

### The following examples work with half angles:

Prove:

Prove: