Variation 1 · answer guide

Trigonometric identity — Cosine square, doubled angle

Question

Which integral is equivalent to ?

This practice question was inspired by Question 2 in the 2021 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: apply the named identity first and simplify before integrating or solving.. With : .
Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: Average value of over a period is , matching the constant term.

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