Double and Half Angle Identities
See Trigonometry Angle Sum Identities – GeoGebra for a derivation/proof of the angle sum identities 1. and 2. above.
In this activity, we start with these angle sum identities and use them to prove the other 10 identities related to doubling or halving the angle. The power reducing identities 7 and 8 are in the form that is needed in integration problems in Calculus II.
We illustrate numerical verifications and formal algebraic proofs. We can also visualize some of the quantities as areas of rectangles related to the unit circle diagram on the right. We also provide an animation giving an area visualization for cos(2A) identity 3 above. Note this illustration/animation works with A in (pi/2,pi). The animation sets A = 5pi/6.