Show that cosθ(9tanθ+4tanθ)≡5sinθ+4sinθ\cos \theta \left( 9 \tan \theta + \frac{4}{\tan \theta} \right) \equiv 5 \sin \theta + \frac{4}{\sin \theta}cosθ(9tanθ+tanθ4)≡5sinθ+sinθ4 for θ≠nπ2\theta \neq \frac{n\pi}{2}θ=2nπ, where nnn is an integer.
Hence solve, for 0<x<2π0 < x < 2\pi0<x<2π, the equation cosx(9tanx+4tanx)=12sinx−2\cos x \left( 9 \tan x + \frac{4}{\tan x} \right) = 12 \sin x - 2cosx(9tanx+tanx4)=12sinx−2 giving your answers to 3 significant figures.
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.