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 ≡ cos2A – sin2A
    or
    cos 2A ≡ 2cos2A – 1
    or
    cos 2A ≡ 1 – 2sin2A
    tan 2A ≡ (2 tan A) / (1 – tan2A)

Example 1

The following examples work with half angles:

Trigonometry Identities - half angles (1) : ExamSolutions - youtube Video

Example 2

Trigonometry - Identities half angles (2) : ExamSolutions - youtube Video