Double-angle identities · derivation ·proof
Where sin 2x = 2 sin x cos x comes from
Spot the pattern in a product. Going the other way is the useful skill: whenever you see sin x cos x, multiply and divide by 2 and the double-angle form appears. This is how ∫sin x cos x dx is done in one line.
sin 2x = 2 sin x cos x
Building it step by step
- See sin x cos xTrigger.
- Write it as (1/2)·(2 sin x cos x)Multiply by 2 and divide by 2.
- = (1/2) sin 2xDouble-angle form.
How to recall it under pressure
Re-derive it from the first line rather than searching memory: start from sin(2*x) and do the one algebraic move the derivation above makes. If you need the statement itself, it is on the double-angle identity for sine page.