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0606/21 May/Jun 2026, Question 5: Solving Trig Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Given y = tan³5x, differentiate to get dy/dx in terms of tan 5x, then use that result to solve dy/dx = 0 for 0 ≤ x < 4π/5.

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Part (a) · 4 marks

Find dy/dx for y = tan³5x, giving the derivative in terms of tan 5x.

  1. 1y = (tan 5x)³
  2. 2dy/dx = 3(tan 5x)² × d/dx(tan 5x)
  3. 3d/dx(tan 5x) = 5 sec²5x
  4. 4dy/dx = 15 tan²5x sec²5x = 15 tan²5x (1 + tan²5x)

Answerdy/dx = 15 tan²5x (1 + tan²5x)

Part (b) · 5 marks

Using your derivative, solve dy/dx = 0 over the interval 0 ≤ x < 4π/5.

  1. 115 tan²5x (1 + tan²5x) = 0
  2. 21 + tan²5x = sec²5x ≠ 0, so tan²5x = 0
  3. 3tan 5x = 0, 0 ≤ 5x < 4π
  4. 45x = 0, π, 2π, 3π
  5. 5x = 0, π/5, 2π/5, 3π/5

Answerx = 0, π/5, 2π/5, 3π/5

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