Tangent sum and difference formula: tan(α ± β)
tan(α ± β) = (tan α ± tan β) / (1 ∓ tan α tan β). The numerator takes the same sign as the angle sum and the denominator takes the opposite one. It is the formula behind the angle-between-two-lines result, where the tangents are the two slopes.
Related Sum & Difference identities
Practise it
Reading a formula is not the same as recalling it under time pressure. The workspace drills Sum & Difference 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.