0606/23 Oct/Nov 2025, Question 7: Solving Trig Equations
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 6 marks
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The question, in short
Solve sec²3x + tan 3x − 3 = 0 for x in the range 0° to 120°, giving the angles that satisfy it.
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Solution · 6 marks
- 1(1 + tan²3x) + tan 3x − 3 = 0
- 2tan²3x + tan 3x − 2 = 0
- 3(tan 3x + 2)(tan 3x − 1) = 0
- 4tan 3x = 1: 3x = 45°, 225°, so x = 15°, 75°
- 5tan 3x = −2: 3x = 116.6°, 296.6°, so x = 38.9°, 98.9°
Answerx = 15°, 38.9°, 75°, 98.9°
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