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. A reliable method is to start with the messier side and simplify until it matches the other side.
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
- 4Since sin θ ≠ 0 for this expression, cancel one sin θ: 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.
- One-sided simplification is often the cleanest proof method; keep each algebra step justified.
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