Practice variation 3 of 3

Inverse trigonometric functions — Sec of arctan

Your question

Suppose and for .

(i) Show that .

(ii) Using part (i), or otherwise, show that .

This practice question was inspired by Question 13(c) 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.

Before you check

• Have you stated every choice or assumption?
• Can another student follow each line?
• Did you verify the final result independently?