0606/12 Oct/Nov 2025, Question 10: Trig Identities and Proofs
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Evaluate the definite integral from π/2 to 3π/2 of the sum of two squared expressions, (sin θ + cos θ)² and (sin θ − cos θ)², and determine the integer k such that the result equals kπ.
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Solution · 5 marks
- 1(sin θ + cos θ)² = sin²θ + 2 sin θ cos θ + cos²θ
- 2(sin θ − cos θ)² = sin²θ − 2 sin θ cos θ + cos²θ
- 3Sum = 2(sin²θ + cos²θ) = 2
- 4∫ 2 dθ = 2θ
- 5[2θ] from π/2 to 3π/2 = 3π − π = 2π, so k = 2
Answerk = 2 (the integral equals 2π)
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