Cofunction and even/odd identities · derivation ·proof

Where tan θ = cot(90° − θ) comes from

Build it from the pair you trust. Rather than memorising a third cofunction, derive it by dividing the first two.

Building it step by step

1. Take sin ↔ cos cofunctions
   Those have a geometric proof.
2. Divide
   sin/cos is tan; cos/sin is cot.
3. tan ↔ cot at complementary angles
   Conclusion.

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 cofunction identity for tangent page.

sampled at 800 random anglesSource: OpenStax Precalculus, Ch. 7 · Paul's Online Math Notes, Trig Cheat Sheet · revised 2026-09-26 ·how we check ·accuracy policy ·report an error