Solve, for 0<x≤π0 < x \le \pi0<x≤π, the equation
3sec2x−4tanx=3 3\sec^2 x - 4\tan x = 3 3sec2x−4tanx=3giving your answers, as appropriate, to 3 significant figures.
Show that
sin4θsin2θ−cos4θcos2θ≡1 \frac{\sin 4\theta}{\sin 2\theta} - \frac{\cos 4\theta}{\cos 2\theta} \equiv 1 sin2θsin4θ−cos2θcos4θ≡1is false, and instead prove the identity:
sin4θsin2θ−cos4θcos2θ≡1cos2θ \frac{\sin 4\theta}{\sin 2\theta} - \frac{\cos 4\theta}{\cos 2\theta} \equiv \frac{1}{\cos 2\theta} sin2θsin4θ−cos2θcos4θ≡cos2θ1Wait, correcting the identity format to match difficulty: Prove that
sin5θsinθ−cos5θcosθ≡sin4θsinθcosθ \frac{\sin 5\theta}{\sin \theta} - \frac{\cos 5\theta}{\cos \theta} \equiv \frac{\sin 4\theta}{\sin \theta \cos \theta} sinθsin5θ−cosθcos5θ≡sinθcosθsin4θPractise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) 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.
