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1.8 E: Trigonometry

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Question 148
a.

Use the identity cos⁡2θ+sin⁡2θ≡1\cos^2\theta + \sin^2\theta \equiv 1cos2θ+sin2θ≡1 to prove that tan⁡2θ≡sec⁡2θ−1\tan^2\theta \equiv \sec^2\theta - 1tan2θ≡sec2θ−1.

[2]
b.

Solve, for 0°≤θ≤360°0° \leq \theta \leq 360°0°≤θ≤360°, the equation

tan⁡2θ+sec⁡2θ+5sec⁡θ=2\tan^2\theta + \sec^2\theta + 5\sec\theta = 2tan2θ+sec2θ+5secθ=2

Give your answers to one decimal place.

[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.

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