# How do you find (cos5x+cos4x)/(sin3x+sin2x), if 14x=3pi?

## How do you solve $\frac{\cos 5 x + \cos 4 x}{\sin 3 x + \sin 2 x}$, if $14 x = 3 \pi$?

Jan 16, 2018

$\frac{\cos 5 x + \cos 4 x}{\sin 3 x + \sin 2 x}$

$= \frac{2 \cos \left(\frac{9 x}{2}\right) \cos \left(\frac{x}{2}\right)}{2 \sin \left(\frac{5 x}{2}\right) \cos \left(\frac{x}{2}\right)}$

$= \frac{\cos \left(\frac{9 x}{2}\right)}{\sin \left(\frac{5 x}{2}\right)}$

$= \frac{\cos \left(\frac{27 \pi}{28}\right)}{\sin \left(\frac{15 \pi}{28}\right)}$

=(cos(pi-pi/28))/(sin(pi/2+pi/28)

$= \frac{- \cos \left(\frac{\pi}{28}\right)}{\cos} \left(\frac{\pi}{28}\right) = - 1$