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If $A+B+C=\pi$, then $\cos 2 A+\cos 2 B+\cos 2 C=$
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Verified Answer
The correct answer is:
$-1-4 \cos A \cos B \cos C$
$\begin{aligned} \text { L.H.S. } & =2 \cos (A+B) \cos (A-B)+\left(2 \cos ^2 C-1\right) \\ & =-1-2 \cos C \cos (A-B)+2 \cos ^2 C \\ & =-1-2 \cos C[\cos (A-B)+\cos (A+B)] \\ & =-1-4 \cos A \cos B \cos C .\end{aligned}$
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