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1.8 E: Trigonometry

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Question 56
a.

Show that the equation

6sin⁡θcos⁡θcos⁡θ+sin⁡θ=(4+2sec⁡2θ)(cos⁡θ−sin⁡θ) \frac{6 \sin \theta \cos \theta}{\cos \theta + \sin \theta} = (4 + 2\sec 2\theta)(\cos \theta - \sin \theta) cosθ+sinθ6sinθcosθ​=(4+2sec2θ)(cosθ−sinθ)

can be written in the form

3sin⁡2θ−4cos⁡2θ=2 3 \sin 2\theta - 4 \cos 2\theta = 2 3sin2θ−4cos2θ=2
[5]
b.

Hence solve for 0<x<π0 < x < \pi0<x<π

6sin⁡xcos⁡xcos⁡x+sin⁡x=(4+2sec⁡2x)(cos⁡x−sin⁡x) \frac{6 \sin x \cos x}{\cos x + \sin x} = (4 + 2\sec 2x)(\cos x - \sin x) cosx+sinx6sinxcosx​=(4+2sec2x)(cosx−sinx)

giving your answers to 3 significant figures.

[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