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O-LevelAdditional MathematicsTrigonometry4037/21 · May/June 2017 · Q118 Marks

Prove that sinx(cotx + tanx) = secx.

  1. (i)Prove that sinx(cotx + tanx) = secx.[4]
  2. (ii)Hence solve the equation |sinx(cotx+ tanx)|= 2 for 0° ≤ x ≤ 360°.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [B2] cosx/sinx + sinx/cosx = (cos²x + sin²x)/(sinx cosx) oe B1 for either cotx = cosx/sinx or tanx = sinx/cosx used B1 for correctly placing over a common denominator or for splitting into 3 correct terms not just for stating or working from both sides
  2. [B1] Valid use of Pythagorean identity e.g. cos²x + sin²x = 1
  3. [B1] Simplification to secx (correct solution only) not if working from both sides
  4. [M1] |cosx| = 1/2 soi
  5. [A1] 60, 300 Correct pair
  6. [M1] cosx = -1/2 soi
  7. [A1] 120, 240 Correct pair

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2017 Paper 2 Variant 1, question 11.

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