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Common Mistakes

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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?

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