7.5 Proving Trigonometric Identities

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In a study of mechanical resonance, an engineer models the response of a vibrating system where the amplitude ratio $R$ is determined by an angle of oscillation $θ\theta$ . For $sin⁡2θ≠0\sin 2\theta \neq 0$ , prove the identity

$2θ−tan⁡θ=cot⁡θ2\text{cosec } 2\theta - \tan \theta = \cot \theta$

[4]

Explain why the identity $2θ−tan⁡θ=cot⁡θ2\text{cosec } 2\theta - \tan \theta = \cot \theta$ is not valid for values of $θ\theta$ where $sin⁡θ=0\sin \theta = 0$ .

[1]

7.5 Proving Trigonometric Identities Questions

Practise Edexcel A Level Maths 7.5 Proving Trigonometric Identities with exam-style questions for A Level Maths. 27 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.