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 sin2θ≠0\sin 2\theta \neq 0sin2θ=0, prove the identity
2cosec 2θ−tanθ=cotθ 2\text{cosec } 2\theta - \tan \theta = \cot \theta 2cosec 2θ−tanθ=cotθExplain why the identity 2cosec 2θ−tanθ=cotθ2\text{cosec } 2\theta - \tan \theta = \cot \theta2cosec 2θ−tanθ=cotθ is not valid for values of θ\thetaθ where sinθ=0\sin \theta = 0sinθ=0.
