Practice variation 1 of 3
Inverse trigonometric functions — Sibling identity with sin
Your question
Suppose and for .
(i) Show that .
(ii) Using part (i), or otherwise, show that .
![Graph of $g(x)=\sqrt{1-x^2}$ on $[-1,1]$.](/figures/28a59e3ed6dd.svg)
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?