Double Angle

Double angle formula: sin 2θ = 2 sin θ cos θ

sin2θ=2sinθcosθ\sin 2\theta = 2 \sin\theta \cos\theta

sin 2θ = 2 sin θ cos θ, which drops straight out of the sine sum formula with β = α. It is the substitution that collapses a product of a sine and a cosine into a single term, and the one that makes ∫ sin θ cos θ dθ tractable.

Related Double Angle identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Double Angle questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.