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Montrer que \[\left| \begin{array}{ccc} \cos a & \cos b & \cos c \\ \sin a & \sin b & \sin c \\ 1 & 1 & 1 \end{array} \right| =\sin \left( c-b\right) +\sin \left( b-a\right) +\sin \left( a-c\right) =4\sin \frac{c-b}{2}\sin \frac{b-a}{2}\sin \frac{a-c}{2}\]