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1.8 E: Trigonometry

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Question 114
a.

Use the identity cos⁡2θ+sin⁡2θ≡1\cos^2\theta + \sin^2\theta \equiv 1cos2θ+sin2θ≡1 to prove that cosec⁡2θ≡1+cot⁡2θ\operatorname{cosec}^2\theta \equiv 1 + \cot^2\thetacosec2θ≡1+cot2θ.

[2]
b.

Solve, for 0≤θ≤2π0 \leq \theta \leq 2\pi0≤θ≤2π, the equation

cosec⁡2θ+cot⁡2θ=3\operatorname{cosec}^2\theta + \cot^2\theta = 3cosec2θ+cot2θ=3

Give your answers in terms of π\piπ.

[5]
Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank