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=32
can be written in the form
2sin3θ+9sin2θ−8sinθ=02\sin^3\theta + 9\sin^2\theta - 8\sin\theta = 02sin3θ+9sin2θ−8sinθ=0
Hence 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 x3sinx−22sinxcosx=3tanx
giving your answers to 3 decimal places where appropriate.
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.