
On a :
\[
\cos\left(\dfrac{6\pi}{5}\right)=\underbrace{\cos\left(\pi+\dfrac{\pi}{5}\right)=-\cos\left(\dfrac{\pi}{5}\right)}_{\text{car }\cos(\pi+x)=-\cos(x)}.\]
De plus,
\[
\cos\left(\dfrac{5\pi}{6}\right)=\underbrace{\cos\left(\pi-\dfrac{\pi}{6}\right)=-\cos\left(\dfrac{\pi}{6}\right)}_{\text{car }\cos(\pi-x)=-\cos(x)}=-\dfrac{\sqrt3}{2}.
\]
Donc :
\[
\cos\left(\dfrac{\pi}{5}\right)+\cos\left(\dfrac{6\pi}{5}\right)+\cos\left(\dfrac{5\pi}{6}\right)=\cos\left(\dfrac{\pi}{5}\right)-\cos\left(\dfrac{\pi}{5}\right)+-\dfrac{\sqrt3}{2}=\boxed{-\dfrac{\sqrt3}{2}}.
\]
