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5 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2008 · Paper 2 · Question 3(c)(ii)

Given that A, B and C are the angles of a triangle, prove that sin((A+B)/2) = cos(C/2).

Hence, show that sin A + sin B + sin C = 4 cos(A/2) cos(B/2) cos(C/2).

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Other parts of this question

  1. 3(a)(i)State the values of tan α and tan β.[2 marks]
  2. 3(a)(ii)Without using tables or calculators, find the tangent of the angle between the two lines.[4 marks]
  3. 3(b)(i)Prove that sin 2θ - tan θ cos 2θ = tan θ.[3 marks]
  4. 3(b)(ii)Express tan θ in terms of sin 2θ and cos 2θ.[2 marks]
  5. 3(b)(iii)Hence show, without using tables or calculators, that tan 22.5° = √2 - 1.[4 marks]
  6. 3(c)(i)a)Prove that sin((A+B)/2) = cos(C/2).[3 marks]
  7. 3(c)(i)b)Prove that sin B + sin C = 2 cos(A/2) cos((B-C)/2).[2 marks]

More practice: the rest of this paper · more Trigonometric Functions, Identities and Equations questions · all CAPE Pure Mathematics Unit 1 past papers