◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsTrigonometry4037/21 · May/June 2010 · Q46 Marks

Given that sinx = p and cosx = 2p, where x is acute, find the exact value of p and the value of cosecx.

  1. (a)Given that sinx = p and cosx = 2p, where x is acute, find the exact value of p and the value of cosecx.[3]
  2. (b)Prove that (cotx + tanx) (cotx − tanx) = 1/sin²x − 1/cos²x.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.

  1. [B1] (a) p² + (2p)² = 1 or cot x = 2
  2. [B1] (a) p = 1/√5 or cosec² x = 1 + cot² x ⇒ cosec x = √5
  3. [B1√] (a) cosec x = √5 or p = 1/√5
  4. [B1] (b) cot²x - tan² x oe
  5. [M1] (b) cosec² x – 1 – (sec² x – 1) or other relevant use of Pythagoras
  6. [A1] (b) Correctly reaches conclusion 1/sin²x – 1/cos²x

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2010 Paper 2 Variant 1, question 4.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Additional Mathematics questions

TrigonometryMay/June 20127m

Given that 15cos²θ + 2sin²θ = 7, show that tan²θ = 8/5.

TrigonometryMay/June 20124m

Show that cot A + (sin A) / (1 + cos A) = cosec A.

TrigonometryMay/June 201215m

3 sin x – 5 cos x = 0 for 0° < x < 360°,

Logarithmic and exponential functionsMay/June 20113m

Express lga + 3lgb – 3 as a single logarithm.

Indices and surdsMay/June 20118m

Solve the equation 16^(3x-2) = 8^(2x).

Straight line graphsMay/June 20116m

The points A and B have coordinates (–2, 15) and (3, 5) respectively. The perpendicular to the line AB at the point A…

← Browse all past-paper questions

© 2026 Oracle Prep