Show that the trigonometric identity sin2x1+tan2x≡2sinxcos3x\frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x1+tan2xsin2x≡2sinxcos3x is valid for all x x\,x where the expression is defined.
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=30sin6ϕ1+tan23ϕ\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).
Practise Edexcel A Level Maths 11.3 Using Trigonometric Identities with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.