Exact value of the cosine of 15 degrees from a double-angle formula, in nested surd form
Exact value of the cosine of 15 degrees from a double-angle formula, in nested surd form
IB Year 6 | Grade 12
5 marks
By expressing \(\cos30^\circ\) in terms of \(\cos15^\circ\) using a double-angle formula, find the exact value of \(\cos15^\circ\), giving your answer in the form \(\frac{\sqrt{a+\sqrt b}}{a}\), where \(a\) and \(b\) are positive integers.[5]
Solution:
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Answer:\(\cos15^\circ=\frac{\sqrt{2+\sqrt3}}{2}\), so \(a=2\), \(b=3\)
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