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.
Practise 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.
