Double Angle Formulae Derivation

This is alternative proof-without-words for the A-level double angle formulae.

If you ask me, this is a nicer way to derive them than just say alpha = beta = theta in the compound angle formulae. I suggest getting the students to use the substitution method first and show the circle method to the students who find it easy. If you have a better idea, please tweet me.

This proof relies on the circle theorem: “angle at the centre is double the at the circumference” and right-angled trig.