Power-reducing identities · derivation ·proof
Where cos³x = (3 cos x + cos 3x)/4 comes from
Derive it at x = 0 sanity check. If you cannot remember the sign, test the formula at x = 0 where all three cosines are known.
cos³x = (3 cos x + cos 3x)/4
Building it step by step
- Left at x = 0: 1cos 0 = 1.
- (3 + 1)/4 = 1Plus sign works.
- (3 − 1)/4 = 1/2Minus sign does not.
How to recall it under pressure
Re-derive it from the first line rather than searching memory: start from cos(x)**3 and do the one algebraic move the derivation above makes. If you need the statement itself, it is on the reduction formula for cos³ page.