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 (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.