By writing 3θ=(2θ+θ)3\theta = (2\theta + \theta)3θ=(2θ+θ), show that
sin3θ=3sinθ−4sin3θ. \sin 3\theta = 3 \sin \theta - 4 \sin^3 \theta. sin3θ=3sinθ−4sin3θ.Hence, or otherwise, for 0<θ<π3\displaystyle 0 < \theta < \frac{\pi}{3}0<θ<3π, solve
8sin3θ−6sinθ+1=0. 8 \sin^3 \theta - 6 \sin \theta + 1 = 0. 8sin3θ−6sinθ+1=0.Give your answers in terms of π\piπ.
Using sin(θ−α)=sinθcosα−cosθsinα\sin(\theta - \alpha) = \sin \theta \cos \alpha - \cos \theta \sin \alphasin(θ−α)=sinθcosα−cosθsinα, or otherwise, show that
sin15∘=14(6−2). \sin 15^\circ = \frac{1}{4}(\sqrt{6} - \sqrt{2}). sin15∘=41(6−2).Practise Edexcel A Level Old Maths Trigonometry with exam-style questions for A Level Old Maths. 13 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) 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.