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1.8 E: Trigonometry

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Question 23
a.

Prove that

cosec⁡θcosec⁡θ−sin⁡θ≡sec⁡2θ\displaystyle \frac{\operatorname{cosec}\theta}{\operatorname{cosec}\theta - \sin\theta} \equiv \sec^2\thetacosecθ−sinθcosecθ​≡sec2θ

[4]
b.

Hence solve, for 0<θ<2π0 < \theta < 2\pi0<θ<2π, the equation

cosec⁡θcosec⁡θ−sin⁡θ=2tan⁡θ\displaystyle \frac{\operatorname{cosec}\theta}{\operatorname{cosec}\theta - \sin\theta} = 2\tan\thetacosecθ−sinθcosecθ​=2tanθ

Give your answers in terms of π\piπ.

[3]
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.

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