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A-LevelMathematicsTrigonometry9709/32 · Feb/Mar 2020 · Q57 Marks

Show that cos 3x / sin x + sin 3x / cos x = 2 cot 2x.

  1. (a)Show that cos 3x / sin x + sin 3x / cos x = 2 cot 2x.[4]
  2. (b)Hence solve the equation cos 3x / sin x + sin 3x / cos x = 4, for 0 < x < π.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

  1. [B1] Express LHS correctly as a single fraction
  2. [M1] Use cos(A+B) formula to simplify the numerator
  3. [M1] Use sin 2A formula to simplify the denominator
  4. [A1] Obtain the given result.
  5. [M1] Obtain an equation in tan2x and use correct method to solve for x
  6. [A1] Obtain answer, e.g. 0.232
  7. [A1] Obtain second answer, e.g. 1.80 (Ignore answers outside the given interval.)

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Feb/Mar 2020 Paper 3 Variant 2, question 5.

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