◈ Oracle PrepSign Up Free
A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2024 · Q48 Marks

Show that sec⁴θ-tan⁴θ = 1+2tan²θ.

  1. (a)Show that sec⁴θ-tan⁴θ = 1+2tan²θ.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [M1] Factorise (sec²θ-tan²θ)(sec²θ+tan²θ) Or obtain an expression in cos² θ or sec² θ Or -1 + (2/cos² θ) OE.
  2. [M1] Use of 1+tan²θ = sec²θ (anywhere) The 2 method marks can appear in either order, in which case the 2nd M1 is for expanding (1 + tan² θ)² - tan⁴ θ.
  3. [A1] Obtain 1×(1+tan²θ+tan²θ)=1+2tan²θ Obtain given answer from full and correct working.

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, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 3 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 Mathematics questions

TrigonometryFeb/Mar 20227m

Show that (sin θ + 2 cos θ)/(cos θ - 2 sin θ) - (sin θ - 2 cos θ)/(cos θ + 2 sin θ) = 4/(5 cos² θ - 4)

TrigonometryFeb/Mar 20227m

Show that sin 2θ cot θ – cos 2θ = 1.

TrigonometryFeb/Mar 20226m

The angles α and β lie between 0° and 180° and are such that tan(α + β) = 2 and tan α = 3 tan β.

DifferentiationFeb/Mar 20178m

The function f is defined for x ≥ 0 by f(x) = (4x + 1)³ᐟ².

FunctionsFeb/Mar 201710m

The functions f and g are defined for x ≥ 0 by f : x → 2x² + 3, g: x → 3x + 2.

DifferentiationFeb/Mar 201711m

The point A (2, 2) lies on the curve y = x² – 2x + 2.

← Browse all past-paper questions

© 2026 Oracle Prep