A robotic arm's joint efficiency factor EEE is modelled by the formula E=cotβ−tanβE = \cot \beta - \tan \betaE=cotβ−tanβ, where β\betaβ is the angle of the joint. Prove that for sin2β≠0\sin 2\beta \neq 0sin2β=0,
cotβ−tanβ=2cot2β \cot \beta - \tan \beta = 2 \cot 2\beta cotβ−tanβ=2cot2βExplain why the identity cotβ−tanβ=2cot2β\cot \beta - \tan \beta = 2 \cot 2\betacotβ−tanβ=2cot2β is not valid when sinβ=0\sin \beta = 0sinβ=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.