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Sum of two cosines as a product, used to find an exact product of cosines

Sum of two cosines as a product, used to find an exact product of cosines

IB Year 6 | Grade 12
6 marks
  1. Show that \(\cos A+\cos B=2\cos\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right)\).[4]
  2. Hence determine the exact value of \(\cos82.5^\circ\cos52.5^\circ\).[2]

Solution:

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Answer:(b) \(\frac{\sqrt3-\sqrt2}{4}\)

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