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Question 175
a.

Prove the identity sin⁡2x1+cot⁡2x≡2sin⁡3xcos⁡x\displaystyle \frac{\sin 2x}{1 + \cot^2 x} \equiv 2 \sin^3 x \cos x1+cot2xsin2x​≡2sin3xcosx

[3]
b.

Hence, show that 4sin⁡4θ1+cot⁡22θ=8sin⁡32θcos⁡2θ\displaystyle \frac{4 \sin 4\theta}{1 + \cot^2 2\theta} = 8\sin^3 2\theta \cos 2\theta1+cot22θ4sin4θ​=8sin32θcos2θ

[1]
c.

Hence, find ∫4sin⁡4θ1+cot⁡22θdθ\displaystyle \int \frac{4 \sin 4\theta}{1 + \cot^2 2\theta} d\theta∫1+cot22θ4sin4θ​dθ

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

855 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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