Half angle formula: tan(θ/2), both radical-free forms
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
Common questions
What is the tan θ/2 identity?
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.
When do you use the tan θ/2 identity?
Use the first form when sin θ is comfortably non-zero and the second when cos θ is near −1.
Which identities are related to tan θ/2?
tan θ/2 belongs to the Half Angle group. The identities used alongside it most often are sin θ/2 and 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.
Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.