
\begin{enumerate}
\item $\begin{aligned}[t]
\cos(x)=-\dfrac{\sqrt3}{2} & \iff \cos(x) = \cos\left(\dfrac{5\pi}{6}\right)\\
& \iff x = \dfrac{5\pi}{6} \text{ ou }x=-\dfrac{5\pi}{6} \quad \text{sur }]-\pi;\pi].
\end{aligned}$

\medskip

L'ensemble solution est donc:
\[
\boxed{ \mathcal{S} = \left\{ -\dfrac{5\pi}{6}~;~\dfrac{5\pi}{6} \right\} }
\]

\item $\begin{aligned}[t]
\sin(x)=\dfrac{\sqrt2}{2} & \iff \sin(x)=\sin\left(\dfrac{\pi}{4}\right)\\
& \iff x = \dfrac{\pi}{4}\text{ ou }x = \dfrac{3\pi}{4}\quad\text{sur }]-\pi;\pi].
\end{aligned}$

\medskip

L'ensemble solution est donc:
\[
\boxed{ \mathcal{S} = \left\{ \dfrac{\pi}{4}~;~\dfrac{3\pi}{4} \right\} }
\]
\end{enumerate}
