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← 2025 HSC Extension 1 paper Question 11(c)

Variation 1 · answer guide

Trigonometric identity — Product-to-sum integration

Question

Find .

This practice question was inspired by Question 11(c) in the 2025 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: apply the named identity first and simplify before integrating or solving..
  2. Simplify the previous line carefully, keeping exact values where possible.Integrate each sine term.
  3. Finish the calculation, then check that the result meets the question’s conditions..
  4. State the final answer clearly in the form the question requested.Final answer:

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Differentiating the answer returns .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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