Solve, for 0<x≤π0 < x \le \pi0<x≤π, the equation
3sec2x−4tanx=33\sec^2 x - 4\tan x = 33sec2x−4tanx=3
giving 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 1sin2θsin4θ−cos2θcos4θ≡1
is 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≡cos2θ1
Wait, 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≡sinθcosθsin4θ
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions, 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.