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Question 107
a.

Show that the trigonometric identity

sin⁡2x1+tan⁡2x≡2sin⁡xcos⁡3x \frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x 1+tan2xsin2x​≡2sinxcos3x

is valid for all x x\,x where the expression is defined.

[3]
b.

In a wave mechanics simulation, the rate of change of energy density E E\,E with respect to phase ϕ\phiϕ (in radians) is modeled by the equation:

dEdϕ=30sin⁡6ϕ1+tan⁡23ϕ \frac{dE}{d\phi} = \frac{30 \sin 6\phi}{1 + \tan^2 3\phi} dϕdE​=1+tan23ϕ30sin6ϕ​

Hence, determine the general expression for E(ϕ)E(\phi)E(ϕ).

[6]
Markscheme

Integration Questions

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

864 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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