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1.8 E: Trigonometry

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Question 61
a.

In a study of mechanical resonance, an engineer models the response of a vibrating system where the amplitude ratio RRR is determined by an angle of oscillation θ\thetaθ. For sin⁡2θ≠0\sin 2\theta \neq 0sin2θ=0, prove the identity

2cosec 2θ−tan⁡θ=cot⁡θ 2\text{cosec } 2\theta - \tan \theta = \cot \theta 2cosec 2θ−tanθ=cotθ
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b.

Explain why the identity 2cosec 2θ−tan⁡θ=cot⁡θ2\text{cosec } 2\theta - \tan \theta = \cot \theta2cosec 2θ−tanθ=cotθ is not valid for values of θ\thetaθ where sin⁡θ=0\sin \theta = 0sinθ=0.

[1]
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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