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+sinθ4for 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 - 2 cosx(9tanx+tanx4)=12sinx−2giving your answers to 3 significant figures.
137 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, 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. Each one has a worked solution and a mark scheme showing where the marks go.