# How do you find the exact value of cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)?

Feb 16, 2016

$\frac{\sqrt{3}}{2}$

#### Explanation:

This is of the form $\cos \left(a - b\right) = \cos \left(a\right) \cos \left(b\right) + \sin \left(a\right) \sin \left(b\right)$

The above expression simplifies to

$\cos \left(2 \frac{\pi}{9} - \frac{\pi}{18}\right)$
$\cos \left(3 \frac{\pi}{18}\right)$

$\cos \left(\frac{\pi}{6}\right) = \cos 30 = \frac{\sqrt{3}}{2}$

Dec 25, 2017

$\textcolor{red}{\frac{\sqrt{3}}{2}}$

#### Explanation:

we know that
color (cyan)(cos (A-B)=cosA×cosB+sinA×sinB)
similarly the equation given is question can be written as
$\cos \left(2 \frac{\pi}{9} - \frac{\pi}{18}\right)$
$\cos \left(\frac{4 \pi - \pi}{18}\right)$
$\cos \left(3 \frac{\pi}{18}\right)$
$\cos \left(\frac{\pi}{6}\right)$
cos ((180°)/6)
color (green)(cos (30°) = sqrt3/2)