In any triangle \( A B C \), prove the following: \[ a \cos A+b \cos B+c \cos C=2 b \sin A \sin ...

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In any triangle \( A B C \), prove the following:
\[
a \cos A+b \cos B+c \cos C=2 b \sin A \sin C=2 c \sin A \sin B
\]
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