# Question #8b831

Feb 12, 2017

$\cos 15 = \cos \left(45 - 30\right)$

expanding by using

$\cos \left(x - y\right) = \cos x \cos y + \sin x \sin y$

#### Explanation:

$\cos \left(45 - 30\right) = \cos 45 \cos 30 + \sin 45 \sin 30$

use the standard angle values for cosine and sine

$\cos \left(45 - 30\right) = \frac{\sqrt{2}}{2.} \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2.} \frac{1}{2}$

factorise

$\cos \left(45 - 30\right) = \frac{1}{4} \sqrt{2} \left(\sqrt{3} + 1\right)$

multiply $\sqrt{2}$ into the bracket to arrive at required solution

$\cos \left(45 - 30\right) = \frac{1}{4} \left(\sqrt{6} + \sqrt{2}\right)$