# How do you find the exact value of cos pi/6 cos pi/3 - sin pi/6 sin pi/3?

Aug 10, 2018

$0.$

#### Explanation:

Recall that, $\cos x \cos y - \sin x \sin y = \cos \left(x + y\right)$.

Hence, with $x = \frac{\pi}{6} \mathmr{and} y = \frac{\pi}{3}$, we have,

$\cos \left(\frac{\pi}{6}\right) \cos \left(\frac{\pi}{3}\right) - \sin \left(\pi 6\right) \sin \left(\frac{\pi}{3}\right)$,

$= \cos \left(\frac{\pi}{6} + \frac{\pi}{3}\right)$,

$= \cos \left(\frac{\pi}{6} + 2 \frac{\pi}{6}\right)$,

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

$= \cos \left(\frac{\pi}{2}\right)$,

$= 0$.