Variation 3 · answer guide

Inverse trigonometric functions — Tan inverse increasing

Question

For real , which is always true?

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. is strictly increasing on .
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: Derivative everywhere.

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