0606/23 May/Jun 2026, Question 12: Solving Trig Equations
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 7 marks
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The question, in short
Solve cosec²2x + 2/tan 2x = 1 for x in the interval −π/2 ≤ x ≤ π/2.
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Solution · 7 marks
- 1cosec²2x = 1 + cot²2x, and 2/tan 2x = 2 cot 2x
- 21 + cot²2x + 2 cot 2x = 1 ⇒ cot 2x(cot 2x + 2) = 0
- 3cot 2x = 0: 2x = ±π/2 ⇒ x = ±π/4
- 4cot 2x = −2 ⇒ tan 2x = −1/2, with −π ≤ 2x ≤ π
- 52x = −0.4636 or 2x = π − 0.4636 = 2.678
- 6x = −0.232 or x = 1.34
Answerx = −π/4, −0.232, π/4, 1.34
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Also searched as: 0606/23/M/J/26 · 0606_s26_qp_23 · 0606 s26 23 · question 12.
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