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If $x+y+z=180^{\circ}$, then $\cos 2 x+\cos 2 y-\cos 2 z$ is equal to
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Verified Answer
The correct answer is:
$1-4 \sin x \cdot \sin y \cdot \cos z$
$\begin{aligned} & \cos 2 x+\cos 2 y-\cos 2 z \\ & =2 \cos (x+y) \cos (x-y)-2 \cos ^2 z+1 \\ & =2 \cos (\pi-z) \cos (x-y)-2 \cos ^2 z+1 \\ & =1-2 \cos z\{\cos (x-y)-\cos (x+y)\} \\ & =1-2 \cos z 2 \sin x \sin y=1-4 \sin x \sin y \cos z\end{aligned}$
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