Variation 2 · answer guide

Inverse trigonometric functions — Complementary identity

Question

For all , equals

This practice question was inspired by Question 7 in the 2023 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: use the restricted domain and range that make the inverse function single-valued.Standard identity: the two principal values are complementary.
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: Check : .

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