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Triple-angle formula for cosine from a compound angle, and the values of cos theta when cos 3 theta is zero

Triple-angle formula for cosine from a compound angle, and the values of cos theta when cos 3 theta is zero

IB Year 6 | Grade 12
6 marks
  1. By writing \(\cos3\theta\) as \(\cos(2\theta+\theta)\) and using suitable double-angle identities, prove that \(\cos3\theta=4\cos^3\theta-3\cos\theta\).[4]
  2. Given that \(\cos3\theta=0\), find all the possible values of \(\cos\theta\).[2]

Solution:

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Answer:(b) \(\cos\theta=0,\ \frac{\sqrt3}{2},\ -\frac{\sqrt3}{2}\)

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