Grade 11 · CAPS-aligned
Grade 11 Trig Identities — Prove It Without Panicking
The 6 identities you actually need and the 3-move trick for proofs.
Proving identities looks intimidating but it's a closed game: you have six identities to know, and the question always reduces to a small number of patterns. The trick is to never panic — pick a side, simplify it, and trust the algebra.
Why most learners find this hard
Most learners try to work on both sides at once and get tangled. CAPS marking requires you to start from one side and end at the other.
What you'll learn
- Reciprocal identities: cosec, sec, cot
- Quotient identities: tan = sin/cos, cot = cos/sin
- Pythagorean identity: sin²θ + cos²θ = 1
- How to manipulate one side until it equals the other
- Common traps: dividing by zero, losing a negative sign
Worked example
Prove that (1 − cos²θ) / sin θ = sin θ.
- 1Start from LHS: (1 − cos²θ) / sin θ
- 2Use Pythagoras: 1 − cos²θ = sin²θ
- 3Substitute: sin²θ / sin θ
- 4Cancel: sin θ = RHS ✓
Answer: Proved.
Exam tips
- Always pick the messier side to start from — it's easier to simplify than to complicate.
- Write 'LHS' and 'RHS' clearly. Markers look for it.
- Never cross-multiply in a proof. Work down one side only.
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