Show that cosθ(4tanθ+3tanθ)≡sinθ+3sinθ\cos \theta \left( 4 \tan \theta + \frac{3}{\tan \theta} \right) \equiv \sin \theta + \frac{3}{\sin \theta}cosθ(4tanθ+tanθ3)≡sinθ+sinθ3 for θ≠nπ2\theta \neq \frac{n\pi}{2}θ=2nπ.
Hence solve, for 0<x<2π0 < x < 2\pi0<x<2π, the equation cosx(4tanx+3tanx)=6sinx−1\cos x \left( 4 \tan x + \frac{3}{\tan x} \right) = 6 \sin x - 1cosx(4tanx+tanx3)=6sinx−1 giving your answers to 3 significant figures.
Practise Edexcel A Level Maths 7.5 Proving Trigonometric Identities with exam-style questions for A Level Maths. 27 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.