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← 2020 HSC Extension 1 paper Question 11(d)

Variation 2 · answer guide

Trigonometric equation — Sine minus cosine

Question

Express as and solve for .

This practice question was inspired by Question 11(d) in the 2020 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: rewrite the equation into a familiar trig form, solve each branch, then filter by the interval., : .
  2. Finish the calculation, then check that the result meets the question’s conditions..
  3. State the final answer clearly in the form the question requested.Solutions in range: and .

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

Verification: Direct substitution yields at both values.

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

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