Show that the equation
2sinθcosθ3sinθ−2=3tanθ,sinθ≠23 \frac{2\sin\theta \cos\theta}{3\sin\theta - 2} = 3\tan\theta, \quad \sin\theta \neq \frac{2}{3} 3sinθ−22sinθcosθ=3tanθ,sinθ=32can be written in the form
2sin3θ+9sin2θ−8sinθ=0 2\sin^3\theta + 9\sin^2\theta - 8\sin\theta = 0 2sin3θ+9sin2θ−8sinθ=0Hence solve, for −π2<x<π2-\frac{\pi}{2} < x < \frac{\pi}{2}−2π<x<2π
2sinxcosx3sinx−2=3tanx \frac{2\sin x \cos x}{3\sin x - 2} = 3\tan x 3sinx−22sinxcosx=3tanxgiving your answers to 3 decimal places where appropriate.
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.
