If \( A+B+C=2 S \), prove that
\[
\begin{array}{l}
\cos ^{2} A+\cos ^{2} B+\cos ^{2} C+2 \cos A ...
If \( A+B+C=2 S \), prove that
\[
\begin{array}{l}
\cos ^{2} A+\cos ^{2} B+\cos ^{2} C+2 \cos A \cos B \cos C \\
=1+4 \cos S \cos (S-A) \cos (S-B) \cos (S-C)
\end{array}
\]
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