Show that the trigonometric identity
sin2x1+tan2x≡2sinxcos3x \frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x 1+tan2xsin2x≡2sinxcos3xis 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+tan23ϕ30sin6ϕHence, determine the general expression for E(ϕ)E(\phi)E(ϕ).
31 exam-style questions on Edexcel A Level Maths 11.3 Using Trigonometric Identities. Each one has a worked solution and a mark scheme showing where the marks go.