2025 HSC Mathematics Extension 1
Question 11(c):
Trigonometric identity
Integrate using a product-to-sum identity.
How to recognise this question
Question type: advanced trig identities
- The command and notation point to advanced trig identities.
- The requested response is a worked solution.
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
- .
- Integrate term by term.
- .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks 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
Find .
Question 2
Evaluate .
Question 3
Express as .