0606/11 May/Jun 2026, Question 3: Trig Identities and Proofs
Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Show that (3 + 5 cot θ)² + (3 − 5 cot θ)² − 50 cosec²θ simplifies to a constant, for 0 < θ < π/2.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1(3 + 5 cot θ)² = 9 + 30 cot θ + 25 cot²θ
- 2(3 − 5 cot θ)² = 9 − 30 cot θ + 25 cot²θ
- 3Sum − 50 cosec²θ = 18 + 50 cot²θ − 50 cosec²θ
- 4cot²θ − cosec²θ = −1
- 5= 18 + 50(−1) = −32, a constant
AnswerThe expression simplifies to −32 shown
Stuck on a step? Read the free lesson: Trig Identities and Proofs
Practise more trig identities and proofs questions
Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on trig identities and proofs
Also searched as: 0606/11/M/J/26 · 0606_s26_qp_11 · 0606 s26 11 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.