Double angle formula: tan 2θ = 2 tan θ / (1 − tan²θ)

\tan 2\theta = \dfrac{2\tan\theta}{1 - \tan^{2}\theta}

tan 2θ = 2 tan θ / (1 − tan²θ), from the tangent sum formula with β = α. It is undefined when tan²θ = 1, i.e. at odd multiples of π/4, which is exactly where 2θ lands on an asymptote of tangent.

Related Double Angle identities

sin 2θ cos 2θ

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.

Practise Double Angle Open the triangle solver

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