Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.
FURTHER MATHEMATICS
WAEC 2010
Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.
- A. \(\frac{6 + \sqrt{2}}{4}\)
- B. \(\frac{3 + \sqrt{6}}{4}\)
- C. \(\frac{\sqrt{2} - \sqrt{6}}{4}\)
- D. \(\frac{3 - \sqrt{6}}{4}\)
Correct Answer: C. \(\frac{\sqrt{2} - \sqrt{6}}{4}\)
Explanation
\(\cos (x + y) = \cos x \cos y - \sin x \sin y \)
\(\cos (60 + 45) = \cos 60 \cos 45 - \sin 60 \sin 45\)
= \(\frac{1}{2} \times \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}\)
= \(\frac{\sqrt{2} - \sqrt{6}}{4}\)
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