2021 HSC Mathematics Extension 1
Question 2:
Trigonometric identity
Which of the following integrals is equivalent to ?
How to recognise this question
Question type: advanced trig identities
- The command and notation point to advanced trig identities.
- The requested response is a multiple choice.
How to handle it: apply the named identity first and simplify before integrating or solving.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Use the power-reduction identity .
- With : .
- Hence .
- Option A is the cosine-square identity; C and D incorrectly introduce sine.
- Answer: B. (NESA multiple-choice key: B.)
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Which integral is equivalent to ?
Question 2
Which integral is equivalent to ?
Question 3
Which integral is equivalent to ?