In a study of mechanical resonance, an engineer models the response of a vibrating system where the amplitude ratio RRR is determined by an angle of oscillation θ\thetaθ. For sin2θ≠0\sin 2\theta \neq 0sin2θ=0, prove the identity
2cosec 2θ−tanθ=cotθ 2\text{cosec } 2\theta - \tan \theta = \cot \theta 2cosec 2θ−tanθ=cotθExplain why the identity 2cosec 2θ−tanθ=cotθ2\text{cosec } 2\theta - \tan \theta = \cot \theta2cosec 2θ−tanθ=cotθ is not valid for values of θ\thetaθ where sinθ=0\sin \theta = 0sinθ=0.
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.