Common Mistakes
Frequent Errors
1. sin(A+B) treated as sin A + sin B (3.12.B.1). 2. cos(A+B) with + sin sin instead of - (3.12.B.2). 3. Forgetting multiple forms of cos(2A) (3.12.B.3). 4. Incorrect Pythagorean substitution sign (3.12.A.2). 5. Dividing by sin/cos without excluding zeros. 6. Verifying with only one test value and no algebra (3.12.B.4). 7. Rewriting that does not actually simplify the target (3.12.C.1). 8. Ignoring domain on inverse-trig relationships (3.12.A.2).
Why These Happen
Identity forms look similar; students memorize fragments without structure.
How to Fix Them
- Keep sin/cos sum templates visible during practice.
- Derive difference/double from sum once, then reuse.
- Always ask: "Does this rewrite help the next step?"
Avoidance Scripts
- "Sine sum: sin cos + cos sin."
- "Cosine sum: cos cos - sin sin."
- "Rewrite on purpose, not at random."
Quick Self-Check
- Did I use the right identity family?
- Are signs consistent on every term?
- Did I note domain when dividing?