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.
38 exam-style questions on AQA A Level Maths 1.8.8 Proofs with trigonometric identities. Each one has a worked solution and a mark scheme showing where the marks go.