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1.7.22 Proofs involving trigonometric functions (A-level only)

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Question 10
a.

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 sin⁡2θ≠0\sin 2\theta \neq 0sin2θ=0, prove the identity

2cosec 2θ−tan⁡θ=cot⁡θ 2\text{cosec } 2\theta - \tan \theta = \cot \theta 2cosec 2θ−tanθ=cotθ
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b.

Explain why the identity 2cosec 2θ−tan⁡θ=cot⁡θ2\text{cosec } 2\theta - \tan \theta = \cot \theta2cosec 2θ−tanθ=cotθ is not valid for values of θ\thetaθ where sin⁡θ=0\sin \theta = 0sinθ=0.

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1.7.22 Proofs involving trigonometric functions (A-level only) Questions

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