Half angle formula: tan(θ/2), both radical-free forms

\tan\tfrac{\theta}{2} = \dfrac{1 - \cos\theta}{\sin\theta} = \dfrac{\sin\theta}{1 + \cos\theta}

tan(θ/2) = (1 − cos θ)/sin θ = sin θ/(1 + cos θ). Unlike the sine and cosine half-angle formulas these need no ± and no square root - the sign takes care of itself. Use the first form when sin θ is comfortably non-zero and the second when cos θ is near −1.

Related Half Angle identities

sin θ/2 cos θ/2

Practise it

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

Practise Half Angle Open the triangle solver

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