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7.4 Simplifying a cos x +- b sin x

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Question 6
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

7.4 Simplifying a cos x +- b sin x Questions

  1. A Level
  2. /Maths
  3. /7.4 Simplifying a cos x +- b sin x

19 exam-style questions on Edexcel A Level Maths 7.4 Simplifying a cos x +- b sin x. Each one has a worked solution and a mark scheme showing where the marks go.

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