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0606/12 May/Jun 2025, Question 4: 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 a definite integral of sin θ from 0 to π, and prove a trigonometric identity involving sec α, cot α and tan α for 0 < α < π/2.

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Part (a) · 2 marks

Find the value of the definite integral of sin θ between the limits 0 and π.

  1. 1∫ sin θ dθ = −cos θ
  2. 2[−cos θ] from 0 to π = (−cos π) − (−cos 0)
  3. 3= 1 + 1 = 2

Answer2

Part (b) · 3 marks

Show that sec α divided by (cot α + tan α) simplifies to sin α, given 0 < α < π/2.

  1. 1sec α/(cot α + tan α) = (1/cos α)/(cos α/sin α + sin α/cos α)
  2. 2Denominator = (cos²α + sin²α)/(sin α cos α) = 1/(sin α cos α)
  3. 3= (1/cos α) × sin α cos α
  4. 4= sin α

Answersec α/(cot α + tan α) = sin α shown

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