2020 HSC Mathematics Extension 1
Question 12(d):
Trigonometric identity
Find .
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
- Product-to-sum: with , .
- So .
- Integrate: .
- Evaluate: at : ; at : .
- Difference: .
- NESA: 3 marks correct; 2 for a correct primitive; 1 for using product-to-sum.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 3 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
Evaluate .
Question 2
Evaluate .
Question 3
Evaluate .