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O-LevelAdditional MathematicsTrigonometry4037/12 · May/June 2014 · Q14 Marks

Show that (cos A)/(1 + sin A) + (1 + sin A)/(cos A) can be written in the form p sec A, where p is an integer to be found.

  1. Show that (cos A)/(1 + sin A) + (1 + sin A)/(cos A) can be written in the form p sec A, where p is an integer to be found.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [M1] M1 for obtaining a single fraction, correctly
  2. [M1] M1 for expansion of (1 + sin A)² and use of identity
  3. [DM1] DM1 for factorisation and cancelling of (1 + sin A) factor
  4. [A1] Al for use of 1/(cos A) = sec A and final answer
  5. [M1] M1 for multiplying first term by (1 - sin A)/(1 - sin A)
  6. [M1] M1 for expansion of (1 − sin A)(1 + sin A) and use of identity
  7. [M1] M1 for simplification of the 2 terms
  8. [A1] A1 for use of 1/(cos A) = sec A and final answer

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 1 Variant 2, question 1.

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