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\begin{exercise}
Simplifier les expressions suivantes:%

\begin{align*}
A  &amp; =\cos(\pi-x)+\cos(-x)+\sin(\pi+x);\\
B  &amp; =\sin(\pi+x)-\cos(x+\pi/2)+\sin(\pi/2-x);\\
C  &amp; =\sin(\pi/8)-\sin(3\pi/8)+\sin(5\pi/8)-\sin(7\pi/8).
\end{align*}


\emph{Indication pour le }$C:$ on remarquera que: $\pi/8+7\pi/8=3\pi
/8+5\pi/8=\pi.$
\end{exercise}


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