Cofunction and even/odd identities · derivation ·proof
Where tan(−θ) = −tan θ comes from
Odd divided by even. Rule of thumb worth remembering: a ratio whose top flips sign flips sign too.
tan(−θ) = −tan θ
Building it step by step
- top: odd, bottom: evensin is odd, cos is even.
- ratio: odd−a/b = −(a/b).
- tan(−θ) = −tan θApply to θ.
How to recall it under pressure
Re-derive it from the first line rather than searching memory: start from tan(-x) and do the one algebraic move the derivation above makes. If you need the statement itself, it is on the tangent is odd page.