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Solving sin 3θ = sin θ without losing solutions

Solving sin 3θ = sin θ without losing solutions

IP 3
7 marks
  1. Using the addition formulae, show that \(\sin(A+B)-\sin(A-B)=2\cos A\sin B\).[2]
  2. Hence solve \(\sin3\theta=\sin\theta\) for \(0\le\theta\le2\pi\), giving exact answers.[4]
  3. A student divides both sides of \(\sin3\theta=\sin\theta\) by \(\sin\theta\) first. Explain which solutions are lost.[1]

Solution:

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Answer:(b) \(\theta=0,\ \dfrac{\pi}{4},\ \dfrac{3\pi}{4},\ \pi,\ \dfrac{5\pi}{4},\ \dfrac{7\pi}{4},\ 2\pi\) (c) \(\theta=0,\ \pi,\ 2\pi\)

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