WAEC - Further Mathematics (2010 - No. 2)
Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.
\(\frac{6 + \sqrt{2}}{4}\)
\(\frac{3 + \sqrt{6}}{4}\)
\(\frac{\sqrt{2} - \sqrt{6}}{4}\)
\(\frac{3 - \sqrt{6}}{4}\)
설명
\(\cos (x + y) = \cos x \cos y - \sin x \sin y \)
\(\cos (60 + 45) = \cos 60 \cos 45 - \sin 60 \sin 45\)
= \(\frac{1}{2} \times \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}\)
= \(\frac{\sqrt{2} - \sqrt{6}}{4}\)