Show that the equation
3cosθ−2=5sinθtanθ 3\cos \theta - 2 = 5 \sin \theta \tan \theta 3cosθ−2=5sinθtanθcan be written in the form
8cos2θ−2cosθ−5=0 8\cos^2 \theta - 2\cos \theta - 5 = 0 8cos2θ−2cosθ−5=0Hence solve, for 0≤x<π0 \le x < \pi0≤x<π,
3cos2x−2=5sin2xtan2x 3\cos 2x - 2 = 5 \sin 2x \tan 2x 3cos2x−2=5sin2xtan2xgiving your answers, where appropriate, to 2 decimal places.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.