Simplify, evaluate if possible using the unit circle: cos(pi/9)cos(pi/18)-sin(pi/9)sin(pi/18) ?

Simplify, evaluate if possible using the unit circle: $\cos \left(\frac{\pi}{9}\right) \cos \left(\frac{\pi}{18}\right) - \sin \left(\frac{\pi}{9}\right) \sin \left(\frac{\pi}{18}\right)$ I can put this in all sorts of formats using half and double angle formulas, but I don't know what is the "most simple" or how to evaluate it using the unit circle. Help? Thanks!!

May 6, 2018

See below

Explanation:

Most simple technique would be to recognize that this is the cosine sum identity:

So:
$\cos \left(\frac{\pi}{9}\right) \cos \left(\frac{\pi}{18}\right) - \sin \left(\frac{\pi}{9}\right) \sin \left(\frac{\pi}{18}\right) = \cos \left(\frac{\pi}{9} + \frac{\pi}{18}\right)$

$\cos \left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$