Sum and difference identities · derivation ·proof
Where tan(A − B) = (tan A − tan B) / (1 + tan A tan B) comes from
Sign bookkeeping. Learn the sum version; get the difference version by flipping B's sign in one place.
tan(A − B) = (tan A − tan B) / (1 + tan A tan B)
Building it step by step
- Top: + becomes −tan B flips sign.
- Bottom: − tan A tan B becomes +Product with the flipped sign.
How to recall it under pressure
Re-derive it from the first line rather than searching memory: start from tan(a - b) and do the one algebraic move the derivation above makes. If you need the statement itself, it is on the tangent of a difference page.